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.
Was "tissue" ever a trademark? Did you mean "Kleenex"?
FWIW, "Kleenex", "Coke", and "Google", all still have their protected status. "Aspirin" was once a trademark (of Bayer?), but is no longer.
https://www.businessinsider.com/google-taser-xerox-brand-nam...