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?

I suppose they're technically archaepronouns, given their age

I looked up whether Ancient Hebrew used pronouns, apparently they did with a bolded "yes." I find this really interesting though too:

The Tetragrammaton[note 1] is the four-letter Hebrew-language theonym יהוה (transliterated as YHWH or YHVH), the name of God in the Hebrew Bible. The four Hebrew letters, written and read from right to left, are yod, he, vav, and he.[note 2][1] The name may be derived from a verb that means 'to be', 'to exist', 'to cause to become', or 'to come to pass'.[2]: 40 [3][4]

While there is no consensus about the structure and etymology of the name, the form Yahweh (with niqqud: יַהוֶה) is now almost universally accepted among Biblical and Semitic linguistics scholars,[note 3] though the vocalization Jehovah continues to have wide usage, primarily in Christian traditions.[5][6][7] In modernity, Christianity is the only Abrahamic religion in which the Tetragrammaton is freely and openly pronounced.

The books of the Torah and the rest of the Hebrew Bible except Esther, Ecclesiastes, and (with a possible instance of יה (Jah) in verse 8:6) the Song of Songs contain this Hebrew name.[6]

Observant Jews and those who follow Talmudic Jewish traditions do not pronounce יהוה nor do they read aloud proposed transcription forms such as Yahweh or Yehovah; instead they replace it with a different term, whether in addressing or referring to the God of Israel. Common substitutions in Hebrew are אֲדֹנָי (Adonai, lit. transl. 'My Lords', pluralis majestatis taken as singular) or אֱלֹהִים (Elohim, literally 'gods' but treated as singular when meaning "God") in prayer, or הַשֵּׁם (HaShem, 'The Name') in everyday speech.

https://en.wikipedia.org/wiki/Tetragrammaton

That's a lot of checkmarks.

There's nothing new ("Neo") about that. It's been common practice for a long time. They don't cover it in public schools since it takes time away from crayon art.

Wouldn’t that be more like urpronouns?