"And the women were being assertive, not rude or abusive. "
Frankly if someone spoke to me like that I would feel uncomfortable and intimated.
"What does the law of that area say?"
Here you go:
abc7.com/wi-spa-protest-trans-rights-koreatown/10857589/
The spa added that it complies with California law, Civil Code section 51(b), which provides that "All persons within the jurisdiction of this state are free and equal, and no matter what their sex, race, color, religion, ancestry, national origin, disability, medical condition, genetic information, marital status, sexual orientation, citizenship, primary language, or immigration status are entitled to full and equal accommodations, advantages, facilities, privileges or services in all business establishments of every kind whatsoever."
Also turns out there were 5 in total who were injured in the resulting protests (which were deemed unlawful by police who dispersed them). This includes 2 victims being stabbed by anti-trans protestors.