So, we have a few alternatives:

1. No filters at all.
2. Full gating (if you didn't went through the prerequisite courses, you're out).
3. Instructor's approval.
4. Entry tests.
5. Big warnings about prerequisites.

I think the best way is probably a mix:

• If you took (and passed) the prerequisite courses, you can enter.
• Otherwise, you pass the entry test (if available).
  • Above some threshold, you can enter.
  • Below some threshold, you're toast.
  • Between them, you need instructor approval.

The idea is to make prerequisite courses optional, while keeping the actual proficiency of the prerequisite material mandatory.