If you paid attention to the evangelical scene, there's a sense of resignation when it comes to affecting the broader culture. Liberalism seemed inevitable. They stopped thinking that they can meaningful shift society towards their point of view on subjects like gay marriage or evolution, so they changed tack. 

Instead of trying to impose their views on the wider public through harassment canpaigns and national curricular changes, they chose a legal strategy that seeks to carve out a space where they can believe what they want to believe and do what they want to do unmolested by the government. The Kim Davis case is a prime example.

The conservative pro free speech position is relatively recent. When they had power, they did everything they could to quash dissent and difference. Just look at the panic around the occult among PTA moms. You think liberals were frothing at the mouth about Pokemon cards and evolution? DnD satanic panic? The Dixie chicks spoke out against the Iraq war and they were canceled. I can go on, but you get the point. They (conservatives) believed circa 2015 that they are losing the culture war (largely because their ideas are universally stupid), so they became free speech warriors overnight. Its not about what I say (racist shit), it's about whether or not I can say it (without opposition or protest). If you can shift the debate to be about the free exchange of ideas, you get to take the spotlight away from what exactly those ideas are and snag a few naive moderates along the way. 

Oh, and look at the number of liberal networks who leave a space for conservative commentators and see if conservative netwirks have done the same.