There seem to be multiple different discourses that are being all conflated together (not by you, but by people who engage in this topic in general).
The first discourse seems to be coming from the "Nashideans" and "Calhounians" that you seem to referencing for most of your post as "hashtaggers". These are the people posting anti-immigrant content and saying they were in the Americas before anybody else, distancing from Africa type of content. And I understand you are not saying all Black americans think this way and that your post was specifically referencing them and their rhetoric. These people are a loud and amplified by the nature of social media. As you know, they are not mainstream opinion. For example, if you had some famous mainstream Black american person, say Michelle Obama, start posting Nashidean and Calhounian rhetoric, it would cause a community meltdown from the absurdity. It is understandable if people are chronically online, like many on Twitter and Tiktok seem to be, that they may think otherwise.
The second discourse is just saying Black Americans need their own ethnic identifier that can't be conflated with other groups. The Black population in America has become so diverse, that Black and African-American are not specific enough by name. It has nothing to do with not claiming black or claiming exclusive ownership of blackness. Just that on the forms where you mark your race, underneath the "Black or African-American" section, just have a designated ethnic identifier, similar to already present ability of immigrant descended populations being able to identify their country of origin with the use of 'X-American'.
I also agree with your first paragraph in the quote that referenced that people who claim their nationality outside of the United States are not distancing themselves from shared African ancestry. So, I am then confused about the notion with claiming a nationality as "wanting to be with white people"? This rhetoric is not given to other black populations throughout the Americans who are also minority populations within their countries that have various levels of antiblackness. If an Afro-Colombian claims Colombia, are they distancing themselves from Africa? Its not as if "new world" black populations are first generation immigrants who are suddenly choosing to completely cut ties with the countries they originate from. Their ancestral roots are from Africa, but their contemporary ethnoculture was literally formed in those American countries. If they were to suddenly claim/speak on Africa with a position of actual belonging, and not just being of African descent (though sometimes even this is enough, with questioning the legitimacy/usage of the term "African-American"), the gatekeeepers would come out and remind them that they are American. Descendents of immigrants who grow up outside of Africa are well aware of this interaction, so why would it be any different for Black Amerians or other populations. Their nationality and claim to such is not in question.
Since Black Americans have been a race-focused people, due to their race-focused environment, their resulting Pan-African philosophy has always been that black people are global population. Some live in Africa, some in Americans and Caribbean, some in middle east, etc. This philosophy has sometimes gotten pushback of "lumping people together" and "projecting their idea of blackness onto other peoples", for various reasons. But they have also been proud Americans who take pride in what their ancestors fought for. That has nothing to do with wanting to "live with white people" any more than it does for other minority black populations in other countries that are proud of their nationalities.
This was just a casual post.
Feel free to correct me if I am misinterpreting. But as far as the hashtag people, I feel we are in agreeance.