Regardless of what the CB says, the HS sets the rules. If they set a physics prereq, feedback from CC users won’t change that.
To answer the OP’s question, no, you don’t need AP Physics 1, but you should have a prior physics course of some type. If C were just the mechanics portion, I would say it’s possible to take it as a first course, since it does duplicate a lot of material from APP1.
However, when C is Mech + E&M, you are now taking one of the few AP courses that matches college courses in terms of pace. Given that everyone else in the class will have had a prior physics course, you will likely be behind the learning curve from the beginning. And don’t expect the teacher to slow the pace to accommodate you if you fall behind.