Why is social conservatism generally associated with religion? I have not read the entire thread, so please forgive me if this has been covered, but I think it needs to be clarified as to which religion(s) is generally associated with social conservatism (assuming we are looking at this question through an American-lens). Most Jews, for example, lean liberal. Indeed for the last 100 years of US elections, Jews have overwhelmingly voted for the Democratic nominee.
However, if we focus on Christianity in particular, and its association with modern social conservatism, then this alliance has been well documented in the book One Nation Under God: How Corporate America Invented Christian America by Kevin Kruse. Kruse delineates the emergence of Conservative Christianity as a form of propaganda orchestrated by the business class during the 1930s in order to vilify and vitiate FDRs New Deal, which the business class saw as a threat towards Capitalism. FDR often used religious symbolism and direct quotes from scripture as apologia for the New Deal, and the worried business class sought to appropriate Christianity as a pro-Capitalist religion, and utilized the help of prominent preachers to help do so.
There is really nothing "inherent" in religion that would cause it to lean socially liberal or socially conservative in their modern day political implications. The current association is simply the result of about 90 years of business propaganda. Interestingly however, many modern businesses do seem to lean towards social liberalism at least as a PR move (e.g. Kellog's refusal to advertise on Breitbart, or various companies celebrating gay pride etc.)