It's amazing how motivated reasoning and a poltics poisoned mind can be used to make obvious points out to be unreasonable. Institutional neutrality is simple, the organization does what is ncessary to operate, but doesn't prescribe anything unnecessarily over that.
It does not mean that professors are not allowed to talk about disagreeable things that are required for teaching the subject. If anything, it makes it easier for them to do so, as they can teach whatever is necessary to produce well-functioning members of society.
Eg you don't need to endorse a specific candidate to fulfill your duty of teaching students. You don't need to avoid talking about research that runs counter to the organization's politics. You don't need to openly pick sides on protests besides advocating for enough civilty to allow your institution to keep operating, and so on. I'm fairly certain that a good portion of the neutrality statements from universities have been coming from the difficult ideological situation presented by the flaring up of the Israel-Gaza conflict, where picking sides opens them up to either being islamophobes or antisemites.
I'm not really sure what you're getting at with the tension about creationism as part of science education. In my schooling the early science education often covered the history of the topic, which would inevitably talk about the local religious ideas, working it's way through them, sometimes even with brief readings of some associated stories, through to major discoveries that provided the evidence for the modern consensus. That's just part of providing a comprehensive education and connecting it to the culture kids are exposed to?