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.