I'm aware of the (sadly ongoing) practice of female genital mutilation, but from what I understand, the purpose of such is not to permanently render someone unable to reproduce, as is the case with castration.
Was it possible to sterilize women safely with pre-modern technology? Was it ever a widespread practice? What cultural role did it serve, if any?
No, it is not possible to make "female eunuchs" prior to modern surgery. So not possible I picked it for my April Fool's post! :) The female reproductive system can be rather more temperamental than the male, but it is very internal, which makes it hard to mess with.
Women were effectively prevented from reproducing in other ways though, usually by simple seclusion. For example, in 18th century Italy, sort of as a counterpart to the castrati, many women were cloistered away in nunneries, sometimes against their will by their families, sometimes voluntarily out of personal conviction. Celibacy has a high failure rate as they say, but it is an effective "sterilization" if you can manage it.
This of course does not count out the possibility of otherwise physically standard female bodies having liminal genders in various societies. The majority of the world's liminal gendered roles are on the male side of things (some physically are eunuchs, some not) but there are a few examples of liminal genders that can be filled by those more on the female side. Unfortunately everything I know about that is about on the level of Wikipedia.