Mmmh AI is gonna make this a real tricky problem. It was bad enough when people would pull edited / low quality clips from movies as "proof". Blech.
When I was young I did have a reasonably sceptical head on my shoulders, but I was also dysphoric as fuck and wistful and I wanted it to be real. So much that I'd find myself subconsciously biased towards giving "p-shifters" the benefit of the doubt, hoping against impossibility that maybe it was true.
But a lot of people, when they throw around claims like this, will treat it like some secret the world is keeping from you that only they know. If you see someone like that? Run the fuck away. Doesn't take much for that to morph into, "Only we know the secret. If you want it, you have to join us. You have to be loyal to us, and do what we say, to prove yourself worthy." And that's where you get p-shifter cults. Creepy as fuck. (And yes, they were real, and probably still are).
Now: if you ever do find yourself really wondering, or just... hoping against all reason that maybe, any of it is true: I'll tell you what I did. Maybe it'll serve you as well as it did me.
Like. Try to physically shift. You'll feel stupid and ridiculous, but give it an honest go anyway. It's a pretty straightforward way satisfy the curiosity. If we really did have some shapeshifting ability hidden in us, you wouldn't need some creep online to activate it, right?
It won't work, and that sucks! But you got that answer for yourself, y'know? Close the case on your own evidence.
I had some of my most vivid mental and phantom shifts when I said fuck it and tried to physically shift. And that was a valuable experience in itself! But in the mirror: no fur, no paws, just the stark reality that we live in a world which is bound to logic and physical laws, and it's only in our minds that we're free from that.
But the closure helps, I think. And sometimes the best way to get that is from yourself.
Beyond that? Logic will snuff out any lingering doubts if you let it. Not just in physical law, but in how people are. There's no way something like that, if possible, would remain secret. And even if someone was trying to hide it: bureaucracy is inefficent and clumsy, people are loose-lipped and crave attention, and a trait like that scattered across random people would not be easy to suppress. The more people you're trying to organise, the harder it is! Like any conspiracy theory, one of the biggest plot holes is always going to be that people are just evidentially shit at keeping secrets.
Finding a way to cope with the longing is the harder work, though. The idea of p-shifting is an easy out, but a poisonous one (and false, completely and utterly false). When you rule that one out, you're stuck with the reality of things and that can feel pretty miserable.
It does get easier, though. You'd be surprised how much healing you can find just in accepting that you're stuck like this and deciding to make the best of it anyway.
You have your mind, and that's a really solid resource! If you want to "really" experience shapeshifting, you can try teaching yourself to lucid dream, for one! (It worked for me. I think it'd work for most people, though maybe not folks with aphantasia). Meditative visualisation is also surprisingly good for this, it just takes a lot of practice.
And there's way to find comfort in the physical world too. Sometimes it's just little things... integrating a bit of your species' body language, or focusing more on a sense you associate with it. Or if you wanted to get adventurous, there's fursuiting and furry lifestyling and LARPing and so on!
I guess, when I closed the door on the idea of fantastical magic existing in this world, I started to be able to notice the subtle, mundane magic of humanity and increasingly, I appreciate it. Even if it does feel weird, too. There's so much potential in the lives we have as human-bodied creatures. It might not make the pain go away deep down, but it can soothe it, and (given the impossibility of the ideal option), I think that's something worth chasing.