As I've mentioned before, I am a philosophy professor. In the courses I teach, I think I hear these two questions from students more often than just about any other typical question. The trouble with these questions is that, aside from being multiply ambiguous, they are usually the wrong sort of question to ask. Sometimes, they are not even questions at all. Let's consider the first one:
Who's to say? (and it's cousin, "Who is he/she to say...?")
On the face of it, perhaps this question is an attempt to determine which people in the world have the intellectual or moral authority to make certain claim, such as, "except in rare and extreme circumstances, abortion is immoral." If that were so, then perhaps a response like, "moral philosophers who have a solid command of the literature are the ones to say in this case," should suffice. (Sometimes I give a similar answer when we're discussing John Stuart Mill's claims regarding how one can know which of two pleasures is more worthy of pursuit.) But, this answer doesn't usually placate the student. I think the reason for this is that the student is not, in fact, asking a genuine question as much as they are using a question to express their disdain for some view that they reject. More importantly, the question (whether a genuine one or not) seems misguided in that, ultimately, it doesn't matter who is making the claim at all. If we're trying to think carefully about important questions, then we should be focusing on why a person makes the claims they do. That is, we ought rationally to be more concerned with understanding and thinking through the reasons that a person might give for or against a particular stance on some issue.
Who are we to Judge?
As with the first question, sometimes this probably isn't a real question at all, as much as it is a way of saying, in effect, "don't judge me," or, "I don't like the idea of saying that X is morally wrong." Ironically, the people most likely to say this are usually the same people most likely to make self-undermining claims like, "you shouldn't try to tell people what is right or wrong." However, if it *is* a legitimate question, then perhaps the best answer is, "we are human beings with the capacity to understand and evaluate reasons for or against a particular claim, and the ability to, sometimes, make correct judgments." Or, if the question is about what gives a person the right or authority to make some judgment, then we are back to asking about what reasons a person has for making a certain judgment on an issue, in which case it doesn't matter who "we" are per se.