Nonbelievers have a strong interest in free speech and a free press, particularly where freedom to publicly criticize religion in concerned.
This is particularly clear in Islamic contexts, where religion is socially very powerful. Since censorship is usually deployed by the powerful in protection of their interests, it’s understandable that Muslim countries are often in the lead in attempts to suppress mockery and criticism of religion.
In the United States, religion is not quite so powerful now—perhaps this is why we enjoy a greater latitude in confronting religion compared to, say, the nineteenth century with its Comstock laws and so forth. But this doesn’t mean that freedom of speech and a free press are not matters of concern in the US. Reporting and criticism involving powerful corporate and government interests have a way of being directly and indirectly suppressed.