What did I miss?

You missed the inevitable arms-race between mimics and legitimate signalers. We're in an evolutionary environment, and assuming that any communication can be taken at face value is a kind of naïveté.

If you want to construct an argument where state's rights (or women sensibly protecting themselves) is important, you have to spend extra effort in your signaling. You need to START by explicitly acknowledging all of the things you might be accused of, BEFORE you present your actual point. You then have to specifically display all of the ways in which your point differs from the false (dog-whistle) signal. For example:

We have too much centralized legislation, and states should be more autonomous. And yes, I know the last time someone said that he was implying that segregation was okay. But I'm seriously talking about the denotation of 'states' rights' here, and obviously 'not being super racist' is part of the stuff I'm not proposing to leave up to states, like, duh. So about giving states more power...

This is the wrong order, and expends insufficient effort in its signaling process to demonstrate that it is not a false signal. This works better:

"A. Most state's rights arguments are, in fact, racist dog-whistles. Unfortunately, some actual, legitimate situations in which states' rights are being trampled upon are swept under the rug, due in part to the poisoning of the discourse by those very dog-whistles.

B. Here is why states should be more autonomous...

C. Here is how we prevent the abuses of state autonomy that happened in the past, while rescuing the needed autonomy that I'm advocating..."

Your system starts with B, then inserts a weak form of A, then jumps back to B - while nearly-completely ignoring C. This is insufficient to distinguish you from a false signaller. By providing a good A, B, and C, you establish that you are willing to expend effort to not be seen as a false signaller (A), clearly present your position (B), and indicate that you recognize the dangers of the false signalers' agenda and are willing to help fight against it as a concession to getting the things you want (C).

Does all that make sense?