The phrase "may god" exists in many languages where the speakers are largely followers of one of the Abrahamic religions. Also, the phrase claims there is one god which goes against Slavic polytheism idea of multiple gods. I just don't see how they are related.

Well, not quite.
They're referring to one god.
This in no way means that they are claiming the others don't exist, they're talking about a god, the one that gives.