The same OP of that thread called a biracial person in this thread a "half cracker" to dismiss their discomfort with posts they feel are hateful or self-hateful.
I think we should be able to recognize that there is a line crossed by some of these posts where they aren't really jokes anymore, and actually reflect essentialist ideology. that's a lack of theoretical understanding, and worse, a lack of kindness and empathy for different perspectives.
I find this idea appealing on paper but I think in practice it is way too individualist and idealist.
I am white, and if tomorrow I decided that I am not a white person at all but instead my particular nationality and ethnicity, absolutely zero conditions for me would change. I would still be privileged in a court room, in an interaction with police, in a job interview, in receiving healthcare, etc. regardless of my personal feelings on my identity. I would be socially understood as white no matter what. White is a social category, not a choice. If I did decide this, absent massive societal change, I would just be denying social reality. Is that actually helpful?
I don't think it is possible to have an individual disidentification with whiteness which would mean anything to other people and to society. It's putting the cart before the horse. The concept and identity of white will disappear when the conditions that make it a meaningful distinction disappear, not when many people decide individually that they no longer belong to it.