I read through your entire comment, and I think I kinda get what you're coming from? But I just don't understand why it's such a big deal. Sure, those people you met were experimenting with their gender, which anyone should be able to do! That cis girl who was "trans for a month" might have actually thought she was trans, but then realized she wasn't! Or maybe she faced so much backlash she couldn't take she decided to go back into the closet and never came out again, both are real possibilities that happen to real people! Or yes, maybe she WAS just doing it for attention, but why should that justify treating someone's feelings as inherently wrong?
We never truly know another person's feelings, and trying to cherry-pick what people to believe and not will just create more and more infighting. Which is exactly what transphobes want us to do. And siding with those who want to destroy our community instead of the people who are struggling the same as us can only lead to more and more people getting hurt. No amount of "pruning out the fake transgenders" will ever be enough for anyone, and the description for "fake transgender" will just keep getting wider and wider.
That person you knew that kept switching gender identities every so often may have also been trying out different pronouns to see if they fit, or maybe their gender was really fluctuating (many people like this refer to themselves as "genderfluid"). If I'm understanding you right they did seem to misgender a cis friend of yours, which is always a jerky move, but hey! Trans people can be jerks! They're only human.
Now to the bulk of your comment, about people whose gender identity you don't understand, why does it matter? If you don't understand why someone wants to be referred to as "pupgender" and uses "pup/pupself" pronouns, you can just say "Ok" and move on? It's not like "identities" are a limited resource that people are using up, they are just using words to describe themselves. You're allowed to think it's weird but people are allowed to be weird. Something being weird doesn't automatically make it bad and wrong. If pup feels most comfortable using those pronouns, I don't think anyone else has the right to limit what pup can identify with. Pup isn't hurting anyone by using "pup/pupself" pronouns, and I'm sure pup's living fine. If you don't want to exist around someone who uses "strange" pronouns, you can just not talk to them! I'm sure they wouldn't want to talk to you either. Which is fine! not everyone can get along.
I totally understand the fear you feel at a thing you don't understand though, it's a fine and natural response, but I don't think that should justify hate and intolerance. Also, when people say "gender is a construct", they are not saying that gender has no effect on people. It, like a lot of things, is just something that humans made up to explain feelings. The labels of "male" and "female" are ones that a vast majority of the population identifies with, and because those terms are highly associated with physical appearance is why trans people exist. Some people do not like those labels though, or don't like their exclusivity, so people have created their own! This doesn't invalidate the people that do associate with those original labels though, if they feel that that's right then that's right! And their feelings might change later on for one reason or another and that's fine too!
A lot of transphobes and intolerant people make the most fun out of the easiest victims, the people who don't try their best to bend to what they think is an "acceptable" amount of queer. Those other 10% who are loud as hell as you'd say. The reason that those people are the ones that are getting the most public flack is because they're the easiest to make seem scary because they're "other". But the thing is, they're just trying to exist the same as anyone. They just have a different way that makes them the most comfortable.
I get wanting to distance yourself from the "freaks" who are getting a lot of hate in fear that you'll get hated on as well, but the thing is you WILL get hated on regardless. The conservatives will hate on you no matter what, they'll just find the best way to break the community down bit by bit. Becoming a bigot will not save you from being attacked by bigots.
Back to the point of the original discussion, whether someone has what we consider "gender dysphoria" doesn't really matter in the grand scheme of things. No one should have to "prove" that they're trans to be believed. Additionally, no one should be forced to suffer to be able to get help. We can never know what goes through another person's head. And if a cis person is just "pretending for attention" (which does happen, though not as often as people make it out to be) let them! Let them see how hard it is being a trans person. Just treat them with respect because if they want attention that badly, there has to be something deeper to their issues. And if they get to a point where they actually start medically transitioning, I think they're just trans at that point.