Tons of great stuff over at Julian's today. In this post, he seems to be asking in part (he says a lot more) whether one can be a culture warrior and a good Rawlsian political liberal at the same time. If that's the question, then I think the answer is: yeah, sort of.
The point of public reason is not that one cannot attempt to change people's comprehensive conceptions in public. It is that when we are deliberating together about the public principles by which we are all going to be governed, we should ideally appeal to reasons that most people can endorse.
I do think there is a kind of rhetorical problem or tension when one shifts from publicly arguing over comprehensive conceptions (“There is no God! Free will is a lie! You are continuous with the apes!”) to publicly arguing about political principles in Rawls-approved tones. If you're perceived as an aggressive flack for a particular comprehensive view, people will have a hard time taking you seriously when you attempt to set out an argument designed to appeal even to the very people you've just publicly accused of being dangerously blinkered. People will suspect you're being tricksy, trying to pull a fast one.
So it's probably tough to be a well-known comprehensive gladiator and a trusted voice of public reason all at the same time.