It's all about worshipping make-believe fictional deities anyway. However, I don't believe they are all the same 'character'. Even between the OT and NT the nature of the 'God character' of both changes radically.
Mormons have a 'Jesus' in their stuff, but he's not the same character as he is in the NT. These books are not history or non-fiction.
If that's the case, then you'd be hard pressed to find any two people in the world who worship the same god...because each worships his own idea of what his god is, and no two are alike. And that would be true even of a pair of Episcopalians sitting next to each other on a pew.
If the deities involved are make-believe and fictional, then the whole question of what "the same god" means becomes kind of meaningless.