You're giving (actual) people the opportunity to choose to have healthier families.
- Note that I say 'healthier families' specifically because willfully passing on genetic features that disadvantage your children burdens not just them but your entire family unit.
Depending on where you fall on the fetal personhood debate, preventing someone from existing is much better than killing them. But that doesn't mean the choice can't reveal negative things about society's overall attitudes towards people in those groups. If you're a member of one of these groups, it feels bad to have someone tell you that a fundamental part of your personality is something that ought to be eliminated from society in general.
And of course autistic people and their families often have hard lives, but a large portion of that difficulty comes from social and infrastructure problems. We're not good at building societies that are easy for differently abled people to interact with.
I want to make an analogy that should hopefully make the problem more clear. It's easy to make a case that being gay or transgender socially disadvantages both a person and their overall family unit. Raising a transgender child is going to be harder than raising someone that conforms to strict gender-rules -- you're going to have a few difficult conversations, and you're going to fight with a few systems, and you're occasionally going to have to deal with jerks telling you you've messed up your kid. None of this is right or fair, and we're getting a little bit better, but it's still a problem.
If there was a way to detect someone's future sexual orientation and identity in the womb, would you be comfortable allowing families to make abortion decisions based on that information? If that technology had existed in the 1980s where being transgender was even harder than it is today, would you have been comfortable with it being used then? Would gay and transgender rights have made the kind of progress we've seen if that technology had been available and unregulated?
Given that in this scenario there are two potential children; the one with undesirable_trait_x, and the replacement without it, and one will come into existence and one will not, as a parent, shouldn't you pick the child that will have the happiest life rather than the one that will better serve as canon-fodder in someones ideological crusade?
However, I'm guessing you're actually talking about morality on an individual level -- that it's immoral for an individual parent not to try and guarantee their future child the happiest possible life. The problem is that even though being autistic is hard, having a hard life doesn't necessarily mean having a bad life. Being autistic is hard because autistic people are different, not because autism is inherently an undesirable trait.
Not everyone who is autistic or who has Downs would, if given the chance, flip a switch and erase that part of their personality, and they bristle at the "happy life" argument because they see it as (intentionally or not) just another way for people to imply, "differently abled people will always lead less satisfying lives." See also the controversy in the deaf community over hearing aids, which are a much less dicey proposition than eugenics but still prompt heated arguments sometimes.
As a side note, it's worth mentioning that no one is talking about artificially increasing the number of differently abled people as some kind of "recruitment strategy". Opponents to this kind of genetic selection are talking about just removing that characteristic as a determining factor entirely. It's not any different than banning sex-selective abortions, which is already an entirely normal and relatively uncontroversial policy in multiple developed countries.
Many families with Downs children describe how much joy and love their Downs children bring to the family, how the family members learned to cherish what’s important in life, etc.
These families compared to many families with non-Downs children are quite healthy and arguably not burdened though they experience different challenges than other families.
EDIT: fix quote; change last preposition in second sentence.
While I personally am not entirely sure how I feel about this sort of eugenics, it's worth noting that at the gestational period these genetic anomalies are detected it's far more likely that these fetuses would progress to develop legal personhood than not.
Given our species history of reliance on anomalous individuals I suspect it's unwise to seek further genetic homogenization and better for us to learn to accept those who don't neatly fit societal norms of fitness.