I think the strip-searching thing and the locker room thing isn't really about trying to draw a line and saying, "HERE. Here is where you're really transgender and it's okay." It's about respecting the dignity, privacy, and bodily autonomy of the women involved. A lot of women - not me - are uncomfortable and distressed about being physically touched by a biological male in a professional capacity (pretty much all of us are uncomfortable and distressed about being physically touched in a personal capacity without our consent). There is no amount of transitioning short of having your brain transplanted into a female body that is going to make it okay for them.
In general, if we're drawing lines, I'd say the line between "really transgender" and "bullying poseur" lies somewhere around making real efforts to live life as the gender you're identifying as, and to reasonably pass as same. Mind you, I still very much consider those people to be members of the sex to which they were born; but I will at least entertain the possibility that they are genuinely dealing with dysphoria . . . unless they start yelling and making demands, at which point all bets are off.
"real effort" vs "poser"
I said it before many times, every single leftist agenda is based on a lie. But if you believe, despite all the evidence, that something is not a lie, and if you do accept it without any questioning or proof, you won't care if is a lie any longer. You can see just in this thread how many claims were told, for example: unequal pay, racist laws, dude is skirt is a woman, etc., and one thing you can be sure of is that every single claim was place by exactly the same parson, and without single proof to back those claims.
I'll come back to your reply, but let me rewind it back a little, to Florida parent's right law.
We must allow children to live as children. If a kid's age is in single digit they're too young and naive to handle rhetoric about sex and sexual orientation, and they must be allowed to discover it when they're older and wiser. We're not asking anyone to hide who they are, or to pretend that children don't know who they are, but there is a fine line between education and indoctrination. Discussing nature and identity might seem good, but young children are simply too naive and unsophisticated to understand the "theory" which can only confuse them later on. Young kids are also extremely impressionable and malleable, they might adopt the ideas and beliefs without truly understanding them, and make drastic changes without understanding repercussions.
There is strong defiance to this form of education where teachers with their "rainbow Messiah complex" believe that they doing kids a favor, and if parents want them to stop, well that's just too bad, they won't. This attitude of teachers and school boards create couple of problems, first one is that parents are primary teachers of kids, and kids are ultimately parents responsibility. Second, there is no allowance for constructive criticism, after all... what if the "theory" changes, or what if the teachers are simply wrong? Regardless of which "theory" we are talking about, whether is gender theory, or critical race theory, or systemic racism, or socialism, or communism, when "theory" is based on lies it's destined to backfire and fail. When those lies are presented to kids as the truth, by the very same people that parents entrusted their kids to, those kids are ultimately also destined to fail.
That is how education becomes indoctrination. Education allows for broad range of viewpoints, while indoctrination emphasizes just one. Being able to handle only one point of view is always negative, being social, political, or religious, because it makes conversation awkward, development difficult and society impossible. Teaching kids "theories" that have no scientific standings is not helpful to anyone, especially to kids, because they don't understand what they being taught, and the backlash in their later life will be devastating and counterproductive.
Having said that, and in response to your post, the left is pushing narrative that you are of the gender that you say you are, the moment you chose that gender, and regardless if is day one of growing your hair long, or few years into hormone "therapy", or being post-op, and they all the same and have to be accepted regardless if they're posers or fully committed to their choice. We can all see when someone is fully committed, and even without agreeing with, we could support their choice. Being forced to accept dude with his bulge in woman's swimming suit as a woman, because he says so, is like everything else left is trying to push for is not just anti-science, and anti-women, but just plain wrong.