Most of your replies seem quite reasonable to me. The "what is Critical Race Theory" one is too minimal to be helpful when actually talking in detail about what one feels about Critical Race Theory, but at least it's a start. But one of the other answers leaps out at me as essentially incorrect (even though it has elements of technical correctness).

First, a parallel story.

Suppose you decide to go around punching auto mechanics in the face because you think they deserve it (maybe you think they're nazis). Shockingly, when you do this, the auto mechanics are furious. You decide to name this behavior "auto mechanic face-punch fury". You keep punching auto mechanics in the face, and when they react with fury, you point out to them that they are engaging in "auto mechanic face-punch fury". Oddly, this doesn't calm them down, but whatever. You've gained a valuable new insight about the emotional depravity of auto mechanics!

Of course, everyone sees what the flaw is here: the reaction has nothing whatsoever to do with being an auto mechanic and everything to do with being punched in the face. The "auto mechanic" part of "auto mechanic face-punch fury" isn't a distinguishing characteristic of auto mechanics, but of you, because that's who you've decided to punch. Even if they "deserve" it in a sense because they're swindling and overcharging customers, the reaction still doesn't have anything to do with them being auto mechanics. It's all about the face-punching, which is all about what you're doing to them.

Let's return to white fragility.

People do not respond kindly to attacks on a group with which they identify or are told they should identify with. Charges of injustice are obviously negative, so when you place someone in a group while attacking that group, a hostile reaction from them is to be expected. Even if they know intellectually that they shouldn't be threatened by the attack, that's not how tribe-affiliation responses work. You respond to the attack emotionally first; only later can you think about it. This is exactly the case where so-called "white fragility" is provoked--cases where their group is attacked (with charges of injustice). It's just like auto mechanic face-punch fury in this case.

This doesn't mean that one shouldn't talk about injustice. But it does mean that the reaction doesn't need its own term. It's completely ordinary human behavior.

If you care to try, and even maybe if you don't, it's not hard to provoke "Black fragility", "anti-vaxxer fragility", "pro-vaccine fragility", "libertarian fragility", "Christian fragility", "male fragility", "trans fragility", "gun owner fragility", and so on. All you need is a group, and something negative about some members of the group. Point out the negative characteristics of some members of the group in a way that highlights that the person you're talking to is part of that group, and BAM! Instant fragility.

Now, suppose you do this, and you notice people reacting strongly...and then give a negative label to the reaction of their group: "(group) fragility". Guess what you just did?

(To the specific claim of it mattering that "many white people are accustomed to being treated as individuals", I don't see evidence that it makes much of a difference. You only have to search around social media a little to find people of all races taking great offense to the presentation of completely true behavior or conditions, engaging in denial, shifting of blame, and all the rest.)

For anyone who wants to know more about how people instinctively form tribal allegiances and react to threats to those tribes or their membership in those tribes, I very highly recommend "The Righteous Mind: Why Good People are Divided by Politics and Religion" (Haidt, 2012). (Only a few of the insights are specific to politics.) It is a masterful work of scholarship. It also gives some good tips on how to steer discussions in a more productive direction.

Anyway, in summary (note--I am open to evidence to the contrary if this is wrong, but it must be more compelling than the evidence that it's a standard tribal response):

Q: What is white fragility? Is it really a thing?

Not really; it is a race-specific label for the normal human response to an attack on a group they're identified with. The response happens, but there's nothing white-specific about it except that people use that label when "white" people react that way in debates about racial justice where "whites" are blamed.