As in every StackExchange site, the rules are pretty simple. You should downvote bad questions.
You could read this blog post by Jon Skeet referring to this issue (it's a bit more focused on programming, but the general rules apply everywhere).
If you downvote a question because the user who asked has done something reprehensible, this is not desirable in SE. The reason is, that a question is a question, no matter who asks. Also, "hating" on a user (even if someone promotes or attemps piracy or whatever), is not constructive. A terrible person, can ask a good question that is helpful to others. Judge the question, not the user.
Furthermore, downvoting should always be revised. Downvoting is not the same as in reddit or other websites. It's not simply a means to indicate poor quality, but a means to provide meaningful feedback, and lead to the improvement of a bad question (or its removal).
By downvoting a user, the aforementioned goal is not satisfied. A user that asks a bad question, may learn that it is not constructive and improve, he also has the right (and should) delete or edit bad questions into good ones. Such behaviour should be applauded, not reprimanded because of past "sins".
The aforementioned question is a good one, and even if previous questions indicate that this user is interested in copyright infrigment (I have no idea about this user, hypothetically speaking), it does not matter. This website is about people coming to read answers to their questions, already posted by others, not about a community and its members' relationships.