I have had people IRL who just don't know better and ask questions about this, not knowing much about either topic and I can see why they might superficially think they could be similar.

In particular I had a white liberal friend ask about Rachel Dolezal's experience and how that compares to a transgender experience.

What helped clarify things was to examine where Dolezal's transracial feelings came from:

Dolezal was born at home in 1977, “on the side of the mountain” in rural Montana, to a pair of white Christian fundamentalists called Larry and Ruthanne; they entered “Jesus Christ” on her birth certificate as the only other witness to her birth. From a young age, Dolezal and her older brother Joshua were put to work on the family homestead, weeding vegetables, foraging for berries and hunting elk; in full-length homemade dresses and dog hair sweaters, she “looked like something out of Little House On The Prairie”. Dirt poor and uneducated, her parents lived by the Bible, spoke in tongues and beat her.

“I felt like I was constantly having to atone for some unknown thing. Larry and Ruthanne would say I was possessed and exorcise my demons, because I was very creative and that was seen as sensual, which was of the devil. It seems like everything that came naturally, instinctively to me was wrong. That was literally beaten into us. I had to redeem myself,” she says with a light, mirthless laugh, “from being me. And I never felt good enough to be saved.”

Blond and freckled, “like Pippi Longstocking”, she recalls choosing brown crayons to draw pictures of herself with dark skin and curly hair, like the Bantu women she saw in National Geographic. She would hide in the garden, smear herself in mud, and fantasise that she had been kidnapped from Africa. What she describes as a profound sense of not belonging followed her to school, where the other children wore trainers and had Doritos in their packed lunches, not elk tongue sandwiches. She did everything she could to fit in, picking huckleberries to earn money to buy Nikes, “but I knew I wasn’t one of them. I was always on the fringe.” The only person who really understood her life was Joshua, but he was the favoured child, the son, and her relationship with her brother grew increasingly uneasy.

source

I walked my friend through the story of Dolezal's formation of an African identity as a form of fantasy escapism while living under extremely brutal and abusive conditions, and how this kind of transracial identity seems to have more to do with her psychology and the need for that identity as a coping mechanism than something truly innate or biological. It at least seems like a plausible explanation for where her transracial identity comes from.

Furthermore, you can point out that transracial identities are not a common cross-cultural phenomenon, and scientists have not found a physical basis for anything like a transracial identity, and even further, race itself is not biologically real, so it's unclear what it would mean for someone to have an innate sense of race.

Meanwhile, transgender people have existed throughout human history and across cultures, and scientists acknowledge they are a natural part of human variation, with physical evidence of correlated genetic markers and autopsies of brains that have found consistent differences in trans brains. Furthermore, the current evidence is that gender identity is a biologically real thing, and not able to be altered by psychological and social influences (so you can take someone like Dolezal and make them a different race, but you can't change her gender identity; one is biological, the other isn't).

My friend seemed satisfied with this kind of answer because it clearly delineates why transracial identities are not like transgender identities, and there just wasn't much left to discuss at that point. She just hadn't ever considered it and didn't know much about either topic.

That said, online it is clear that people who want to debate transgender folks with topics like transracial are usually not acting in good faith, so I don't want to dismiss your intuition - I just wanted to offer my experiences with a person IRL who was well-meaning but by coincidence did ask about transracial identities.