Also, in my opinion, you cannot be a member of an oppressed class (as used in class analysis as I define it) if you have the option to just opt out of it.
A working class person cannot identify as millionaire. I mean, they can, but they'll still be as poor as before.
A woman can identify as man, but she'll still be discriminated against in every possible way as long as other people are able to tell her actual sex. (And if she doesn't have her female reproductive organs removed - which leads to lifelong dependence on artificial hormones, so at the very least one medical professional will know her true sex -, she will still be subject to taxes on pads and tampons, as well as oppressed by bans of contraception and abortions)
And if a black person tells a bunch of racists planning to beat them up that they identify as white, three guesses as to how well that is going to work.
To belong to an oppressed class as I define it for the purpose of analysis, you have to be either clearly identifiable (like women and black people) to be targeted with oppression, or it must be possible to discriminate against you on a general level, without knowing what you, as individual, are. ( women and working class).