By whom? Not progressives. It is a standard right-wing a way of attempting to distract from actual progressive statements like “white people, including those who aren't personally racist, are privileged by institutional racism” or “White identity is grounded in racism”.
Also, your second statement maybe applies to the US, but there are many countries where white people are not the majority, or where there were virtually no other races than white. Saying that e.g. Norwegians or Italians are privileged by institutional racism is absurd. I am from a post-communist country that was always 99.9% white, saying that “White identity is grounded in racism” is absurd and of course totally racist.
Sticking my neck out a little, and leaving out my personal positions, I think you are interpreting "White identity" as "any identity held by people who are white", where dragonwriter meant something more like "holding White as an identity"?
Any way you spin it, it is not ok. The color of my skin is my immutable characteristic, any derogatory statement about the whole white race will always be wrong.
You could reasonably argue that I have misinterpreted dragonwriter, that dragonwriter's interpretation doesn't match that of the other progressives who use the phrase, or that there are other problems with that interpretation (I don't, here, even endorse it). But your particular rant is off base enough that I don't think you understood it.
Since we are discussing a distinct American center-left faction’s position on domestic group relations, I don't know why you'd think the positions ought to apply to conditions elsewhere.
If you are talking about a whole race of people, but you actually mean only a specific subset, then it is up to you to define the context, not up to the reader.
(And even in that case you will still probably end up with a racist generalisation.)