CDC -
OK, I watched the Tapper interview. I agree with you on this. If I'm being charitable, I don't think this is willful manipulation of data from the CDC. I think they're probably just being unnecessarily careful in terms of trying to keep the spread down.
Keep in mind that your original claim was that academic institutions "bow to whatever pressures the far left apply to them." I don't think you've provided evidence that the CDC is doing this, and I don't think you've provided evidence that academia as a whole does this.
The focus on "stakeholders" seems strange to me. The word appears three times in the document. Most of the time, the CDC is only saying that schools should be transparent with the data. That seems obvious to me. I don't think the CDC is making these determinations based off of talking to teachers and parents alone, or even primarily. I don't see the evidence that the CDC's determination was motivated by pressure from the left. Watching the interview, it seems to be an absurd degree of caution.
I think it's great that you can attempt to discern whether an individual study is credible. I'd much rather prefer that over broadly classifying all academic institutions as catering to the left. If you have an individual problem with the methodology, point it out.
Trans -
You didn't answer the question. Gender is a question of identity. Why can't someone with a ***** be a woman?
This is Blaire White.

Blaire White is a conservative YouTuber, and is also a trans woman. Blaire White has a *****.
In terms of gender, Blaire is obviously a woman. If you saw Blaire in public, you would immediately assume that she has she/her pronouns. It seems obvious to me that she would not be male in gender.
And of course, I agree that gender has no "objective standard." It's a social construct for a reason.
Either way, I just don't care about the "do trans people exist" debate a whole lot. If we both agree that trans people should be respected and should not be misgendered, if for no other reason than common courtesy, where does your problem lie? What actual harm is being done by the left on the topic of trans people?