The burden of proof tennis is quite tricky here because it's not about whether you claim something exists, it's whether you claim something that goes against what's generally accepted. If I claim quantum mechanics don't exist, it's not on you to prove they do.
And that's before we get into the fact that there isn't a general consensus on whether God (or any gods) exist.
To be clear, I'm not trying to say it's unfair for atheism communities to have those rules. Your community, your rules. But if I'm seeing those posts, I'm going to be bothered, and if I respond, I'm going to break the rules and bother everyone else. Better to not see it in the first place.
In the same way, I'd expect atheists to block a Christian community if it were trending - though I'd be willing to meet them in constructive debate in such a community if the rules permitted it.
Blocking is a community is how I control my personal feed, it's not a condemnation.