I've always found it a little odd that people say the Nazis discredited eugenics, since there is a qualitative difference between sterilizing people, even forcibly, and outright murdering them, and I don't see why you would need the latter to happen in order to see the wrongness of the former.
It's a little like saying "I used to be in favour of banning poetry, until that political party took power and started murdering poets". Surely, the evils of banning poetry should have been evident right from the moment the idea was proposed, without having to see someone taking it to "the next level" in order to get your moral epiphany.
That said, even with the Nazis allegedly serving as a cautionary example, compulsory sterilization, with varying degrees of fidelity to the original eugenic principles, did manage to maintain a certain degree of popularity in certain democraric jurisdictions, eg. the Canadian province of Alberta(until 1972), and even social-democratic Sweden(until 1976). So, yeah, it's possible that, with NO anti-eugenic backlash counterinspired by the Nazis, you might see the western colonial powers try to implement widespread sterilization programs in the third world. Indira Gandhi OTL tried it in India, with not altogether volntary participation, so why not the boys in London, Paris, Brussels etc?
One "problem" might be if anti-colonialism is still a thing in the ATL. I'm guessing that the Mohandas Gandhis and the Jomo Kenyattas wouldn't be too keen on the colonial authorities coming in and forcing all the brown people to get themselves rendered incapabale of reproducing. So it might become a bit of a sore point(no pun intended), exacerbating the tensions between whitey and the natives.