Is it rude to ask the lecturer whether there is any “effective prerequisite”?

I wouldn't phrase it in terms of "effective prerequisites". But it's certainly fine to discuss with the professor whether you are adequately prepared. You could visit their office hours, or send an email:

Dear Professor So-And-So:

I am interested in taking your course MATH 4321. I see that no prerequisites are listed, but I was wondering what background knowledge is expected, and whether I'd be ready for this course. I've taken related courses X, Y, Z and feel comfortable with the material from those courses, and have also had some experience with topic Q. Does this seem sufficient? If you can recommend specific topics to review, or additional reading, I would appreciate it. Or, if there are other courses I should take first, that would also be helpful to know.

If you like you can attach a copy of your transcript.

Think about this from the lecturer's point of view. If you are the lecturer, would you rather:

1. Have a student email you about what the prerequisites are and whether she meets them, or
2. Have a student not email you, enroll, then find out she cannot understand what you are saying at all?

I think most reasonable people would prefer #1. If you are concerned about overpressing and appearing rude that way (e.g. responding to your CS professor with "are you seriously saying this level 4000 CS course has no prerequisites except this very basic OS course??") then you could also ask for details such as the textbook used or perhaps look through homework/tutorials/past-year exam papers, and gauge the level of the course that way.

Its worth noting that some universities attempt to automatically enforce pre-requisites either by machine or by administrative review at the time of enrollment. Some professors may not want formal prerequisites because they can create administrative barriers to enrollment for a student that may have all the necessary knowledge without having some specific course listed on the transcript.

I smacked into this problem from the other side as a student at a University that administratively enforced pre-requisites and where the professors tended to list them explicitly and exactly. I spent a lot of time running around getting professors to sign forms authorizing me to take classes without having the formal prerequisites and it was annoying for me, my adviser that had to process it, and the professors.

With that said, I think asking about "effective prerequisites" using those words might either seem a bit of a challenge to a professor or possibly confuse them as to exactly what you mean. I suspect asking them what prior knowledge is assumed or asking for recommended prior reading is likely to get a positive response.

You can also probably get some idea of whether the class is too advanced or not by flipping through the textbook. If the first couple of chapters make sense you are probably fine. If you encounter unfamiliar terminology and concepts you consider difficult in the first couple of chapters then you should either wait on the class or do some independent study first.