Wondering how to approach the LGBT problem

[Ferd]

I think the right (self protection) approach is to make an inquiry to the school admin what the actual written policy is for gender identification and restroom use is.

make no indication of your bias. simply request the policy for personal understanding.

Then once that is in hand, decide how to proceed.
if the policy is based on actual gender, then report the violation.

if the policy is based on what a person "feels" their gender is, then you have to decide if you want to fight that battle. It may very well be worth the effort to fight the school policy but one has to be prepared to deal with the fallout. which might very well include expulsion.