That's not really the point of what I was trying to show.
Individual parents can/do (as you say) choose tools from different approaches based on the situation and context. I don't think most people IRL would rigidly follow any kind of "parenting style".
But if you're a parenting expert or educator proposing a particular philosophy, or a researcher trying to find out if something is effective/harmful/safe/causes a particular outcome, then it is useful if there is an overarching theory or an agreed-upon definition behind the whole thing - that way people saying well OK, I'm going to try X approach, have something to refer back to, troubleshoot if it's not working etc - and people can openly critique/push back/build upon it etc. There's also a clear definition of whether someone is actually doing it properly or not, so you can have a meaningful discussion around whether X approach works, in what context, for what child/situation/behaviours etc.
And TBH probably for the majority of parents especially if you have NT children it doesn't really matter exactly what you do and you can just muddle through without having to think about things too much. So probably in that scenario the exact label doesn't matter anyway.
But as the situation currently stands because all the examples in my post are real examples of different approaches that people call "gentle parenting" you can see it's impossible to do research on it to say whether it's effective/harmful/etc and if someone says "I do gentle parenting" they might as well be saying "I do flibbertigee parenting" because it is about that useful as a phrase to communicate what they mean to others. They are likely using it as a shorthand to mean (whatever they think it means), but that doesn't work if the other person doesn't have the same definition as they do.
So when you have a conversation like the OP saying "My friend does X and says it's gentle parenting, gentle parenting must be a load of rubbish!" and loads of people insist that the friend is "doing gentle parenting wrong" they are both right and both wrong, because there is no agreed-upon definition of gentle parenting it is an ever moving goalpost, you can't do it wrong because there is no actual method to follow, but you can also never criticise it either. In fact someone gave a really good description of it being "magical unicorn parenting" because the definition shifts all the time so anything that sounds good is suddenly "gentle parenting" and anything that causes harm "well that's not REAL gentle parenting" so you can never live up to it anyway.
Also I think it is divisive, because if you've bought into a label of "I'm doing gentle parenting" then necessarily that is because you think it is different from some other kind of parenting (whether that's behaviourism, or the way your parents did things, or some imaginary idea of a rigid parenting style, or the word "time out", or dismissing feelings, etc etc) then you're likely to dismiss things out of hand which might actually be helpful, or use it as a reason to sneer at other parents, which is unhelpful. (This goes both ways I think).