At different times and places, self-identified “Hindus” have argued that Hinduism teaches:
-belief in many “gods” as well as belief in one Supreme God,
-that there are no mandatory rules and regulations on behavior, and yet moral regulations known collectively as dharma are important and must be followed,
-the doctrine that everyone is equal, and yet there are differences between people due to their different karmas, and
-that spiritual truth is taught in the Vedas and Vedic literatures like the Bhagavad-gītā, and yet the conflicting, non-Vedic beliefs of other religions must be respected and accommodated.
These contradictory statements may attract a variety of casual believers, but they are confusing to the sincere seeker. Is Hinduism really self-contradictory, or does the problem lie in the way different people define “Hinduism?” Examined objectively, one has to admit that there is a tendency to confuse different concepts that are each referred to as “Hinduism.” Specifically, the term “Hinduism” has been used to describe (1) religious traditions originating from, or at least theoretically accepting the authority of, an accepted corpus of canonical texts in the form of the veda-s or some other Vedic literature, and often having flourished well before the Age of British Imperialism, and (2) relatively recent sects of modern origin whose founders mix elements of traditional Hinduism with non-Vedic beliefs and emphasize pluralism and personal intuition over doctrinal consistency or objective authority.
The differences between these two concepts can be understood by examining their linguistic origin and historical usage. The term “Hindu” originated in ancient times when Persians, trying to describe the people living in the region of the Sindhu river, mispronounced the “s” as “h” owing to the limited phonemes of their language.  To them, the “Hindus” were the people living in the area of the Sindhu River, and the word “Hinduism” came to refer to the religious traditions of these Hindus.  These ancient Indians worshiped iconic representations of various deities, performed elaborate religious sacrifices, followed an hereditary class system, and had religious beliefs based at varying levels on Sanskrit scriptures known as the veda-s and their accessory literatures, the Itihāsas, the Purāṇas, and the Dharma-śāstras. Thus, in this particular usage, “Hinduism” referred to the world-view and religious traditions of the Vedas and other literatures upholding the Vedic authority.
However, the modern layman use of the term “Hinduism” encompasses the less orthodox and more heterogeneous beliefs of modern descendants of Vedic Hinduism. These modern beliefs were often inconsistent with the Vedic tradition because they had been influenced by foreign ideologies. The British occupation of India from the 18th-20th centuries resulted in the forced introduction of Christianity with its ideologically xenophobic exclusivism.  The technologically, less-sophisticated Hindus of that time were “educated” in schools developed by their Christian overlords to believe that their Hindu culture was primitive while European Christianity was the path to civilization. [4,5] Lacking the firm, intellectual conviction of the orthodoxy, these modern Hindus were ill-prepared to reconcile their religious beliefs with their resentment of Christian exclusivism, the egalitarian charm of Western humanism, the inevitable modern tendency towards materialism, and the existing diversity of various Vedic and neo-Vedic Hindu traditions. Not surprisingly, they re-imagined Hinduism as a religion that taught objective, spiritual truth yet excluded no contradictory belief, insisted on the equality of everyone while reinventing and rationalizing caste, downplayed the importance of regulated behavior while paying lip service to the significance of dharma, and simultaneously accepted polytheistic and monotheistic points of view as valid. 
Thus, Hinduism in its original usage referred to religious traditions of ancient origin derived from the Vedas and/or Vedic texts like the Itihāsas. Hinduism in its more current usage includes neo-Vedic traditions which incorporate non-Vedic points of view that were a response to Christian imperialism. Herein lies the contradiction. One usage is inherently conservative and internally consistent, while the other usage is heterogeneous in scope and includes religion traditions that are heterogeneous in their origins. Added to this confusion is the fact that many people who identify themselves as “Hindus” may have have beliefs and practices that are not “Hinduism” in the Vedic sense.  They are Hindus in a cultural sense but not in a strictly religious one. However, they may also rationalize their non-adherence to Hinduism in the name of Hinduism, a phenomenon that is particularly characteristic of Neo-Hinduism as well shall see in a future article.
Since the broader usage of the term “Hinduism” is so ambiguous, defining it is problematic. For example, can one’s beliefs be characterized as “Hinduism” if one engages in behavior that is forbidden in the Dharma-śāstras? Is it sensible to characterize one’s beliefs as “Hinduism” if said beliefs are clearly contradicted by the Vedas? Can a school of thought be included within the “Hinduism” umbrella if its founders explicitly reject the authority of the Vedas? If one answers in the affirmative, then at what point does something objectively cease to be Hinduism?
These and other, similar questions point to an unmistakable conclusion: Hinduism, like any other religious term, is not whatever one whimsically deems it to be. Hinduism refers to the religious traditions that derive their authority in some way from the Vedas. To be considered a form of “Hinduism,” a tradition’s followers must at least theoretically accept the authority of the Veda. This is the only definition that is logical and consistent with the term’s historical usage.
References & Notes:
1. http://en.wikipedia.org/wiki/Hinduism#Etymology ‘The word Hindu is derived (through Persian) from the Indo-Aryan/Sanskrit word Sindhu, the Indo-Aryan name for the Indus River in the northwestern part of the Indian subcontinent (modern day Pakistan and Northern India). According to Gavin Flood, “The actual term ‘hindu’ first occurs as a Persian geographical term for the people who lived beyond the river Indus (Sanskrit: Sindhu)”. The term ‘Hindu’ then was a geographical term and did not refer to a religion. Among the earliest known records of ‘Hindu’ with connotations of religion may be in the 7th-century CE Chinese text Record of the Western Regions by Xuanzang, and 14th-century Persian text Futuhu’s-salatin by ‘Abd al-Malik Isami. Thapar states that the word Hindu is found as heptahindu in Avesta – equivalent to Rigvedic sapta sindhu, while hndstn (pronounced Hindustan) is found in a Sasanian inscription from the 3rd century CE, both of which refer to parts of northwestern South Asia. The Arabic term al-Hind referred to the people who live across the River Indus. This Arabic term was itself taken from the pre-Islamic Persian term Hindū, which refers to all Indians. By the 13th century, Hindustan emerged as a popular alternative name of India, meaning the “land of Hindus”. The term Hindu was later used occasionally in some Sanskrit texts such as the later Rajataranginis of Kashmir (Hinduka, c. 1450) and some 16th- to 18th-century Bengali Gaudiya Vaishnava texts including Chaitanya Charitamrita and Chaitanya Bhagavata. These texts used it to contrast Hindus from Muslims who are called Yavanas (foreigners) or Mlecchas (barbarians), with the 16th-century Chaitanya Charitamrita text and the 17th century Bhakta Mala text using the phrase “Hindu dharma”. It was only towards the end of the 18th century that European merchants and colonists began to refer to the followers of Indian religions collectively as Hindus. The term Hinduism, then spelled Hindooism, was introduced into the English language in the 18th-century to denote the religious, philosophical, and cultural traditions native to India.’
2. Of course, the term “Hinduism” was not likely used by the ancient Persians, but the point remains that the English construction of HinduISM implies a set of religious beliefs. It is undisputed that this construction is based on the ancient usage of the word “Hindu” to denote the ancient people living in the Indian Subcontinent, and that these people had religious beliefs based on the veda-s and other sacred literature based on the veda. Therefore, “Hinduism” clearly refers to those religious beliefs.
3. The Bible, John 3:16-18, 36 is quite clear on the doctrine of Christian exclusivism: “For god so loved the world that he gave his only begotten son, that whoever believes in him should not perish but have everlasting life. For god did not send his son into the world to condemn the world, but that the world through him might be saved. He who believes in him is not condemned; but he who does not believe is condemned already, because he has not believed in the name of the only begotten son of god. He who believes in the son has everlasting life; and he who does not believe the son shall not see life, but the wrath of god abides on him.” To Hindus, the idea that one prophet holds the exclusive key to salvation, such that having no belief in him leads to eternal damnation and the wrath of God, is simply not logical or consistent with a Supreme Being who is fair and impartial.
4. The creation of the modern Indian educational system was the brainchild of Thomas Babington Macaulay, a member of the governing Supreme Council of India. Far from being an impartial scholar with a passion for uncovering truth, Macaulay’s pro-European bias and agenda was anything but objective. https://en.wikipedia.org/wiki/Macaulayism: “Macaulay held western culture in high esteem and saw his undertaking as a “civilizing mission“: “We must at present do our best to form a class who may be interpreters between us and the millions whom we govern; a class of persons, Indian in blood and colour, but English in taste, in opinions, in morals, and in intellect. To that class we may leave it to refine the vernacular dialects of the country, to enrich those dialects with terms of science borrowed from the Western nomenclature, and to render them by degrees fit vehicles for conveying knowledge to the great mass of the population,” Macaulay declared.“
5. More on the father of the Indian educational system at https://en.wikipedia.org/wiki/Thomas_Babington_Macaulay,_1st_Baron_Macaulay: “In his view, Macaulay divided the world into civilised nations and barbarism, with Britain representing the high point of civilisation. In his Minute on Indian Education of February 1835, he asserted, “It is, I believe, no exaggeration to say that all the historical information which has been collected from all the books written in the Sanskrit language is less valuable than what may be found in the most paltry abridgement used at preparatory schools in England”.“
6. See http://berkleycenter.georgetown.edu/quotes/swami-vivekananda-on-universalism for one such example. Swami Vivekananda, an 18th-century Indian monk and leader of a newer sect of Hinduism, famously claimed that: “By the study of different religions we find that in essence they are one. When I was a boy, this skepticism reached me, and it seemed for a time as if I must give up all hope of religion. But fortunately for me I studied the Christian religion, the Mohammedan, the Buddhistic, and others, and what was my surprise to find that the same foundation principles taught by my religion were also taught by all religions… We see, therefore, that if one religion is true, all others must be true. There are differences in non-essentials, but in essentials they are all one.” Note the statement is a non-sequitur. One religion being true does not imply that other religions are also true, and as far as foundation principles are concerned, they are most certainly not the same. It is beyond the scope of this article to explore their differences, but most likely we will cover this subject in a future writing.
7. This is not dissimilar to the way many Christians and Jews identify themselves as such even when they are not strict practitioners of Christianity or Judaism. Like the terms “Christian” and “Jew,” the term “Hindu” is also a cultural term by convention, but this point may be lost on non-Hindus trying to understanding “Hinduism.”