I know the Founding Fathers were for religious freedom and tolerance and for the clear separation of church and state. But nowadays religion has such a disproportionate importance in American politics that it effectively makes or breaks a candidate. Can anyone explain what happened in the past two centuries which led to the current state of affairs? Any reading recommendations on the matter also very welcome.
While religion definitely has a significant influence on American politics today, it might be wrong to say it's "become" a huge part of our political culture. Religion has always been a big part of American politics.
There are a number of books that trace the rise of the evangelical Christian movement as a distinct political force -- Earl and Merle Black's Rise of Southern Republicans, and Perlstein's Before the Storm: Barry Goldwater and the Unmaking of the American Consensus come to mind, though the evenhandedness of the latter remains a subject of debate. But for a treatment of the importance of religion writ large, I'd point you to Noah Feldman's Divided by God. Feldman is an influential first amendment professor, and his book, pitched to a popular audience, chronicles the development of religion and religious liberty in the early republic.
Can a historian give us a view on a couple of assumptions in the question:
Were the founding fathers in favour of religious freedom and tolerance?
Were they in favour of clear separation of church and state?
There is a separation of church and state, not a separation of church and politics and there never has been. One example:
"The charge of atheism had been a leitmotif of Hamliton's critiques of Jefferson and the French Revolution. Now he hoped that by publishing pamphlets, promoting charities...this new society would promote Christianity, the Contstitution and the Federalist party..."
--Alexander Hamilton, Ron Chernow