These kind of discussions are very frustrating for people on both sides, because it seems really obvious to everyone that they're right and the other side is wrong. The main way to get someone to understand your point of view seems to be by comparison to similar situations. That leads to a lot of "it's not the same thing" comments, but I think it's still the best way forward for anyone trying to reach common ground in good faith.
So, here's a comparison to think about: for those who think it's wrong for a white person to look, dress, and act like a black person, do you feel the same way about trans-women? They grew up as men, so they haven't suffered any of the disadvantages of being a woman, but now they look, dress, and act like women.
If the answer is that it's different, because these were men who genuinely felt that they should be women and weren't trying to gain money or fame from the change, then is it okay for 'normal' white people to 'blackfish', as long as they aren't trying to profit from it and genuinely feel more comfortable as part of the black community?