I didn't say I believe it or not. This isn't going to be some gotcha about my beliefs, I was explaining to the OP why this kind of thing is controversial.
> what is wrong with a state eugenics program, as long as it is not coercive or manipulative (that is, as long as it is done with the free consent of the parents)?
Well coercive or manipulative are not black-and-white, and there is concern that the line is over stepped. But leaving that aside, I go back to my first post.
Would you have any concerns with a government eugenics program to eliminate trans people from society using genetic screening and abortion counseling informing expectant parents about the horrible disadvantage, discrimination, and horrific physical and mental suffering that they go through at extremely high rates, and assuring them that abortions are a good treatment?
You skipped the question really. It's not where exactly you draw the line with disadvantage and difficulty, and it's not about an individual making their own personal choices. I'm asking about a government eugenics program with such a goal.
Well I don't want this to be a gotcha about your beliefs either, so I don't really need you to answer, the question is more to get people thinking about why the whole issue is not as simple as it seems.
On to the topic itself - I think it depends a lot on the specifics of such a program, and other social context. If it's used in a coercive or manipulative way, and it is also seen as an excuse not to improve things for trans people who are already living, obviously it would be controversial. If it's more informative and optional, and it comes paired with clear proof that the government isn't simply trying to kill the undesirables (such as Healthcare coverage for trans people, protection from discrimination etc), then I believe few would be against it.
Now, could it still be controversial? Sure, apparently casting a black person to play an elf is controversial.
We can probably all agree that screening for certain high-fatality conditions and terminating the pregnancy if they are found is generally better - say, Tay-Sachs disease. We can also agree that screening for other genetic traits and terminating the pregnancy if they are found is unnecessary at best and harmful to society at worst - say, aborting all female genotype fetuses.
Between such extremes lies the realm of the subjective and the messy, where some will agree and some won't. A democratic state may morally/ethically encourage or discourage opinions on these matters, ideally based on the best outcomes for all its citizens.