How many hairs you want to split about this, homie?

It's not splitting hairs. The article says they were fired after they included their pronouns in work emails. The University said no one was fires based only on the pronoun listings.

Those don't contradict. If the pronouns weren't a factor, you would expect the the university to have said that, rather than implying it was one of the factors.

Cherry picking (suppressed evidence, incomplete evidence, argument by half-truth, fallacy of exclusion, card stacking, slanting) – using individual examples or data that confirm a particular position, while ignoring related information or data that may contradict that position.

I don't think you understand what is meant by "data" when in that definition of "cherry picking". The use of pronouns isn't "Data".