Though it is a concern, I'm not overly concerned.
Conservatives of all sorts will be trying to add all kinds of material to the exclusion list, not just the religious ones. It'll be a battle for many different groups to keep their material available, not just the non-religious.
That said, there's always a way round. The internet outside the World Wide Web is almost completely unaffected; torrents and most bulletin boards will carry on regardless. Even banned websites can be accessed using a number of methods: mirrors, proxies, etc.
That's assuming that the new laws are actually enforced in any serious way. Going by precedent, that's not likely.