The sticking point for me is when you add the tag, "3e and 4e feel very different to me, so, 4e isn't really D&D anymore."
That's where I draw the line.
Well, I certainly can't claim to have read every post ever on ENWorld, but I think you are worrying about a bogeyman.
As soon as you add the words "to me", as in "4E isn't really D&D anymore to me", it is about feel. One person comments on their feelings, and then someone else decides that is an absolute. And everything else comes from that break down.
Even if it was me personally talking explicitly about YOUR game, all I can express is my opinion. Frankly, it is impossible for you to play a game of 4E and have ME perceive it as "D&D as I would have recognized it before 4E existed".
Now, if someone insists that they feel the same to them, I'm a bit inclined to think they are just being argumentative. But, if they really insist, so be it, I will take them at their word. But that isn't really a victory, they have simply made it clear that for one reason or another they don't get it the way I do.
Clearly the definition of "D&D" is formally changed. But the context of the conversation is always such that "Pre-4E D&D" is what is being talked about.
If you walked to any person who takes the "doesn't feel like" position and asked them if they wanted to play D&D, a very early question is going to be "what edition?" No one is disputing that D&D is an edition.
But at the same time, back when I would play GURPS I would introduce it to new players as "like D&D". I thought (still do) that there were huge differences between GURPS and D&D (2E at that time). But I also understood that a brand new player would have a general idea of what D&D was and the differences would not be significant to someone brand new. As they played a few times, they would get it and "playing GURPS" would have a different meaning than "playing D&D". But that is a transition from being a total new player to having experience. I'd readily tell a completely new player that PF and GURPS and 2E are all "playing D&D, kinda like 4E." But anyone who is past the completely new phase I would expect to grasp the distinctions.
If someone tells me there are no distinctions then I immediately know they are in that "brand new player" level of perception. People may not like that their perceptions is seen that way. But, sorry, there is no way around it.
People are saying they perceive it differently. And people are clearly suggesting that they don't have a great deal of respect for less discriminating perceptions. But no one is saying those less discriminating perceptions don't exist. They are just saying that they do not apply to people with more discriminating perceptions.
I would say the opposite does not apply. There are people saying they DON'T perceive a difference and that since they don't this somehow proves that a difference doesn't exist and therefore OTHER people's experiences of an actual difference don't exist.