I think progressives almost always win in the long run. Haven't seen too many lately arguing over issues Thomas Becket was willing to die for.I would agree with the concept that both extremes don't care ... except in the same way the a Carlton/Collingwood fan takes being hated by the other people as a validation of their worth...
Your Religious Right (as opposed to religious people) and your Left (not sure what adjective to use there) both have a hankering to make society into their image ... although the Right mostly I suspect feel that they are in a losing battle and the more fundamental end of them pretty much figure they will do their best until the Rapture hits and they get to eject out and Jesus/God gets to clean up the inevitable mess. The left, whose religious sensibilities are distinctly more secular/materialist, tend feel they are on the right-side-of-history (which is part of the religion of progress mythology of course) and aim for an earthly utopia.
Every dream of religious rescue has thus far been in vain (especially the ones that come with dates attached to them!)
Every dream of societal utopia that has been put into practice on a large scale has devolved quickly into tyranny or anarchy.
Where I do find a difference is that your average right-ish Christian type, while convinced that they are right and you are wrong, is happy to let you continue to think differently ... and to pay the consequences later. Your average left-ish proto-utopian insists on unity and thinking the wrong things is not allowed (thought-crime anyone).
Looking at the current debate on whether gender matters (aka the marriage equality survey) there is a definite framing from one side that theirs is the only legitimate option and that anyone who disagrees is not just being disagreeable but hateful, immoral, reactionary, un-progressive and, of course, just wrong.
The republican referendum did not put to rest that issue (and yes I know it was a poisoned chalice) and I don't for a minute think that a 'no' will do anything but make the activists change their tactics and try some other means ... it is just what all evangelist religions do.
Being predominantly made up of people I think both sides behave pretty similarly. Conservatives are just scared liberals and vice versa. Most of them sincerely believe their side is right, most have little to no empathy for, or understanding of, their opponent's arguments and motivations. Most just cheer on each issue like they are supporting their football team.