The issue with abortion is that some think the fetus deserves legal protection because it is equivalent to a human baby. So, they don't think it should be killed. In Italy, abortion is allowed in the first 90 days. After that, it is illegal. These websites were providing abortion pills to be used past the 90 day period, which is illegal.

So, these websites were being blocked because they were engaged in illegal activity.

Would not illegality be handled by charging those suspected of the activity and hearing the case in a court of law?

Maybe those blocking the sites are not acting on behalf of law enforcement but rather their own ideas of legality and morality.