Yeah, but the monarchist protestors want to reinstate the US-backed Pahlavi dynasty in the form of Reza Pahlavi.

His father Mohammad, the last US-installed Shah of Iran has literally said this in an interview:

Women are wicked, evil, all of them ... Women haven’t produced anything, no scientists, they’re pretty creatures

And has repeatedly referred to women as sexual objects existing only for his gratification.

Reza himself has been quiet on women's rights, never once denouncing either his father's views or the currently existing gender inequality in Iran.

I guess it wasn't very socially acceptable to be that misogynistic in the US after the 70s or so. Maybe he will finally speak out now that Trump made this kind of discourse mainstream again.