https://www.bradley.com/insights/publications/2012/04/one-cr...
In my unprofessional opinion, the red cross should go the way of "tissue", "google", "coke", etc. It's too common, hasn't been enforced. You lose the exclusive right to it.
This isn't some bit of copyright law. This is an international treaty that has vested the right to enforce this thing with a specific group. Misuse isn't going to result in in a DMCA takedown. Misuse of the red cross is an international crime, a violation of the Geneva Conventions. Don't like it? Elect people and have them withdraw your country from the Geneva Conventions. I doubt any party anywhere would ever adopt such a platform.