However, race is also socially constructed, so it's tricky. People who claim to be "trans-racial" are still regarded as delusional by society despite this. This is mostly just the position of the society we are in.
But there is something more that makes gender transition more valid than racial "transition": Gender dysphoria is a real condition, that has the medically recommended solution of social and medical transition. This is a good reason for why society should adjust it's social construction of gender, and this is why it is happening right now. To date, "race dysphoria" is not medically recognized and has not been formally observed. It has no history dating back hundreds of years like being transgender does.
This lying to get an advantage can potentially apply to trans people in sports too. People are always claiming that near elite male athletes who can't win in men's competitions will just say they are women to face easier opponents, but we haven't really seen any evidence of that occurring. This is primarily because the obstacles to check a box on a college application are so drastically different than the obstacles in front of someone who wants to publicly and officially change their gender. Considering that, I think the best approach is to not waste too much energy on "fixing" this problem until it is actually shown to be a problem.
For the record, people have self-identified as being Black:
* https://www.nbcnews.com/think/opinion/jessica-krug-rachel-do...
* https://www.theguardian.com/us-news/2017/feb/25/rachel-dolez...
Is there some principled way to decide what things one can self define as and which one can't?