Both Dolezal and transwomen are members of privileged classes wanting to "appropriate" the identity of another oppressed group, both use stereotypes in pursuit of passing

I am transgender. I'm not "wanting to appropriate" the identity of another oppressed group. Appropriation means to take something -- and the usual connotations of the word are negative.

I already am a woman, I never appropriated anything except the male culture which was forced upon me.

Female culture is already my culture, because I'm a woman. I don't need to take anything. It's already mine.

Whether I pass or not does not change my gender identity. My gender is the same regardless, it's only perception that changes.

I also did not ever have any opportunity to choose my gender. It is built into me. I was born a female, I've always been a female, I will die a female, and even if I had not ever begun transition, I'd still be a female, no matter how masculine I might look or what my DNA might say about me.

In regards to "privileged classes", I'd argue any male privilege is massively outweighed by the disadvantages of being a trans woman existing in a transphobic and misogynistic society.

What's the difference between someone wanting to join a race and wanting to change gender?

That's a stupid question because gender and race are too dissimilar to form a meaningful comparison. Don't try to make out like there's some similarity between being transgender and trying to transition to a difference "race" (whatever race even is). There is not.

I say that because there are literally millions of trans people worldwide, whereas there is (afaik) only a single example of a person who believes themselves (rightly or wrongly) part of a different race/ethnic group.

There is also a huge body of corroborating evidence suggesting physiological reasons for why people may be transgender. There is nothing for transracialism. It's not even a topic in the medical/academic community.

You're trying to compare something that exists in practice, with something that only exists in theory.

Not only that but sex/gender is something intrinsic to any isolated homogeneous ethnic group. Racial identity is not. Racial identity only forms in ethnically heterogeneous societies.

In the ethnically homogeneous group a person may be transgender (whether they have the language to understand it or not), but a person can't be born with some physiological reason/ability to identify as an ethnic group they have never even heard of, or come into contact with.

For example, people born in Europe are not born with the knowledge of Asian people. Whereas, people are born with structures in the brain/body that cause (usually) male or female gender identity to form at a young age.

I personally believe there are more gender identities than just the accepted binary, but that's another kettle of fish.

There may be some physiological reason for why a person such as Dolezal identifies as a black person despite her history, but this is not common enough for it to be recognised as a distinct medical condition/phenomenon.

It may happen in the future, but we can't assume that. I doubt it ever will.

So, her example is completely inconsequential.

As far as I can tell, "transracialism" is only a "thing" as far as a child of a substantially different phenotype to the rest of the family is brought up as if their phenotype is not dissimilar.

For example, a Japanese baby brought up in a European family.

I can't think of any other meaningful examples, and this example of "transracialism" would not be due to physiological reasons -- it'd be circumstantial.

I'm sorry but I can't see any way that your argument holds water.