Yes, but parents can turn on content filtering within iOS onto Safari, as well as allow or block websites individually. Other browsers do not implement this filtering.
I know you said "can't" but just to confirm, is there no iOS API to get parental control info to block stuff like this? If not, I wonder why Apple doesn't provide that option.
o/w, "Safari supports parental controls" argument is BS.
Probably the same reason why other browsers can't use adblock addons while Safari can or why other browsers had crippled JavaScript performance until recently. Apple is afraid of losing Safari market share, so they're making preferential treatment to it whenever possible.