The question appears to be: need one accept certain premises of Christianity (whether Protestant or Catholic varieties) in order that the dominant understanding of, say, the secular state and the caste to make sense? That those to whom such accounts make sense do not explicitly subscribe to the premises of a specific religious appears to throw doubt on our claims.
Consider the very distinction between ’the religious’ and ’the secular’. Historically, Christianity has drawn this line. (Theologians have spent much ink over the last two thousand years drawing, defending, and elaborating upon this distinction.) It is also the case that political thinkers in the West, some of whom were militantly atheistic, have made this distinction into a cornerstone of their theories. Further, many Indian thinkers, most of whom know very little of Christian theologies, base their arguments on these and allied distinctions. The existence of the last two groups appears to tell us that even when one rejects some or all religions, even when one is utterly oblivious to the histories and theologies of the Christianities, this distinction does make sense.
There are two possible explanations for this state of affairs. (One could come up with many more but, for the sake of clarity, I will focus upon the two opposing extremes.) One is to argue that for this distinction to make sense no particular background political theory (or any particular set of theologies) is required. Such a distinction, in that case, is a neutral distinction: it is neutral with respect to theologies and political theories. Of course, no distinction like the above, strictly speaking, is neutral. It is rooted in some or another theory, in some or another set of assumptions. (This is the insight we have due to the unflagging labors of the historians and philosophers of sciences and languages.) This claim is familiar to most students of religion.
Suppose that there exists a theory, which argues the following: the distinction between ’the secular’ and ’the religious’ is drawn within a religion, by a religion and that it is a religious distinction. What is called ’the secular’ is religion secularized or is religion in a different set of clothes. That is, it suggests that religions spread in two ways: through the process of conversion and the through the process of winning adherents to its doctrines but by formulating the latter in a ’neutral’ way. Consequently, this theory suggests that the process of conversion and the process of secularization are two faces of the same coin: the spread of a religion. In such a case, the unfamiliarity of people with some or another set of identifiable theological doctrines is not an argument against the claim that these distinctions are theological or religious in nature. The acceptance of theological or religious claims by people who are atheistic and ignorant of religious niceties, in such case, indexes the extent to which a religion has spread in society.
I have built the barebones of such a theory and such an argument. Consequently, if one wants to challenge this, one has to come up with an alternate theory of religion, which does all the work my theory does and something more besides. (Again, this is an insight from the philosophies of the sciences.) A mere reference to the fact that atheistic people or people ignorant of religious matters accept the distinction between ’the secular’ and ’the religious’ is neither evidence nor a relevant argument.
For more, check On the dark side of “Secular”: is religious-secular distinction a binary?