but lets look at your example source of cognitive dissonance, NAACP:

The NAACP has done historically monumental things on behalf of a group of very different people that were being excluded as if they were the same. It comes from a different era and different motivated individuals taking initiative. It predates a different individual pushing “African American” much later on. That predates such rampant subsequent immigration and population growth in the US where enough people find African American to be so ambiguous to the point of ridiculous, while there are many slave descendants that take pride in the term and make it their whole identity (or have it forced on them like many black people in other English speaking countries with no American parents, this is particularly comical to me), whereas others who may also be slave descendants adopt black American or other adjectives and identifiers. With the NAACP there is no utility in changing that acronym and no need to or drive to, like a landmark. It wouldn’t surprise me if they arbitrarily did change the name on their own, but there is no talk or consensus amongst its beneficiaries to do so (unlike other landmarks).

Well, yes, this is how the group forms in the first place. It's made up of people who don't have an identity in common other than the one that's forced upon them of "non-white" by the white people discriminating against them.

Note that in countries which aren't white-majority you don't generally get a group of people holistically identifying as "people of colour", even if the same ethnicities would do so in the US. Instead you get different forms of racial discrimination.

Similarly LGBT+ merges a group of people with very different identities and practices, the primary thing they have in common is receiving the same kind of abuse from the same people.