The history of church-state relations in the United States is a very complicated subject, the kind of intellectual terrain that you could spend several semesters exploring in a graduate degree (as I once did, late in the Vietnam War era). 

In recent decades, roughly the era defined by the rise of the Religious Right, there have been several distinct stages in church-state affairs. At one point, it was rare for thinkers on the left and right to communicate with one another. Then came the Clinton White House years when -- I know this will be hard for some readers to believe -- there was serious progress and constructive dialogue, primarily because conservatives began to enthusiastically embrace the First Amendment. Yes, even though the politics of abortion loomed in the background.

As I wrote in a post early in the Barack Obama administration:

You see, once upon a time there was a wide coalition -- roughly from the ACLU to Pat Robertson -- that was focused on another issue altogether, which was free speech, freedom of association and trying to find ways (think "equal access" laws) that treated religious believers and nonbelievers the same when it came time for them to express their beliefs. ...

It was crucial, you see, for believers and nonbelievers to have the maximum amount of freedom without the government getting entangled (the key word) in determining which doctrines were acceptable and which were not. If the chess team got to use a room after school, then so did Campus Crusade for Christ (or the young atheists circle). 

Can you imagine that kind of truly liberal (in the old sense of that word) coalition existing today, in an era defined by bitter battles about gay marriage and, in a strange healthcare flashback, birth control? I know, it's hard to imagine.