I remember a while ago an American politician said, "God is non-binary", which predictably drew attacks from conservatives.

The Catholics I know (non American here) just kinda shrugged it off. "He's probably trolling, but not exactly wrong", and pointed me to the cathecism.

We ought therefore to recall that God transcends the human distinction between the sexes. He is neither man nor woman: he is God. He also transcends human fatherhood and motherhood.

In the same document they also simply use standard "he/him", nothing like what the meme suggested. The language of "Father", is used to invoke the image of a parent and figure of authority.

Without taking away all the unspeakably horrible things the church has done, as far as theology goes that seems... reasonable?