But...

As for the U.S. version [GINO], that has no bearing on the real Godzilla at all. Godzilla in this (and all the Japanese movies) is male, and Toho has never portrayed him in the films nor in their publicity materials as otherwise.

Yes, Minya is not Godzilla's biological son. Godzilla merely adopts him. Minya is a creature of the same species as Godzilla, or a similar one. You'll notice that Minya's skin is smooth--he does not have the char marks from the atomic bomb that Godzilla has covering his body.

OK...

That's monstrous! So, where's the fun if you only have to get intimate with yourself????

That is not necessarily true. The Japanese language uses gender-neutral pronouns to refer to the monsters, but all English dubs of the films explicitly refer to Godzilla as male. This was Toho's decision starting with the original Godzilla, and all subsequent English dubs have used male pronouns to refer to Godzilla. Toho themselves oversees most of these dubs. Not to mention, English is frequently spoken even in the Japanese versions of the films, and Godzilla is always referred to as male by the characters. Toho has also cemented Godzilla's gender in official media. For example, supplementary materials for Son of Godzilla refer to Godzilla as "Papagojira." The title "King of the Monsters" is officially applied to Godzilla, and is even trademarked by Toho.