It matters what the authority of Government says about an issue. Government opposition makes it illegitimate. Many people care about that and avoid illegitimate things.

Some things should have to be underground, which many will see as a mark of shame for it. Most people don't want to be underground. You seem to take "opposed by the Government" as a badge of honor, which is understandable, but it is not how a majority of people think, especially outside the US.

That may be true for rational thought but belief isn't rational thought. If the Government of the United States decided tomorrow to make believing in Alien Abductions and Crop Circles a law I'd simply be forced to break the law.

That's where the flaw is. The governments of these other countries think they can suppress belief simply by suppressing speech and they can't.

It's not really about suppressing beliefs, it's about suppressing instantiations of those beliefs, especially legitimate organizations that people can be part of and enjoy their life without shame or hiding underground. That discourages many people away from them. Why suppress such organizations, groups, discussion meetups, social circles, etc? Because of the danger of violence.