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.
Beyond preparing you to take any particular AP exam, your HS Physics courses are designed to teach you the subject. And if your HS has a designated sequence, they are likely doing that in a way such that each course builds on the prior courses, and indeed assumes you have taken their version of prior courses.
I would therefore not skip ahead in their sequence unless they actually provide that as a standard option. Like at some high schools, there is a track that leads to AP Physics C that doesn’t go through AP Physics 1, so that’s fine. But if that is not a standard track, I would not push to do it yourself.