Is this sentence correct/natural?

It's OK.

. . . as an atheist.

Anonymousbelongs to

This is strange. Would it not be more natural to word it differently?

You can say it many ways.
He recently told his family he's an atheist.
He recently revealed to his family that ...
He recently let his family know that ...

That doesn't make the original incorrect (once you add the "an").

I wouldn't call it unnatural. You could say 'is part of'.

The word 'household' is correct but somewhat unnatural here. You could say
eg "He is part of a Christian family and he recently came out to them as an atheist."

Sorry - I didn't see the part you were specifically asking about.

If you favor shorter sentences: He recently told his Christian family that he is an atheist.