One of the woke anti-intellectual counterarguments to support “their” or “they/them” as an identifying pronoun is that it is “neutral.”
“They” is not neutral in the sense of grammatical number. “They” can’t be singular. It (referring to the word “they”) is plural.
Strunk & White’s The Elements of Style is the Holy Grail of grammar advice. Touring a fancy private school a few years ago, my group observed a high school English Literature class. The students had read a Charles Dickens work and were writing essays on their individual laptops. I asked the teacher what grammar references the kids used. He responded that they (the kids, plural) simply used apps on their computers. The teacher looked surprised when I asked the question.