Actually, if your body is read as male by the majority of society, you probably have a responsibility to be more open to crying in public and not associating it with shame. You've probably also received countless societal cues from media (even if your dad was cool with it, which he probably wasn't) which associate your crying with shame, so no matter how woke you are, you retain a deep emotional trigger that you have to acknowledge.
But same, tho. I try to not necessarily look to cry in public, and there aren't really a lot of contexts in which I want to cry... but if the tears come, they come. Let them. Don't apologize. Anyone who makes fun of you for crying looks like an asshole.