I asked a professor if I can collect data by method X and he replied : "I am sorry - we do not render such judgments in advance". What does that mean?
To "render a judgement" is to make a decision about whether something is good or bad, acceptable or unacceptable. The term comes from the legal profession. When a judge decides a case, he "renders a judgement". People sometimes use the phrase in other contexts, I guess you could say it's a metaphor or an allusion.
In some cases judges or legal experts will say that they "cannot render a judgement in advance", meaning that they cannot tell you whether something you are planning is legal or illegal until after you do it. If you look at this positively, it means that they can't make a legal decision without seeing all the circumstances. They can't make a decision based on abstract hypothetical cases. If you look at it negatively, they refuse to tell you whether you want to do is legal or illegal, so all you can do is try it and then if they decide it's illegal, you go to jail.
So in this case, the professor is saying that he can't tell you whether what you are proposing to do is acceptable or not. You would have to do it, and then he will read your paper (or whatever the output of your process is) and, based on all the circumstances of what you actually did, decide whether or not it is acceptable.