Public urination is illegal in most places, you get a fine. I wouldn't call it common, I'd call it something that happens in alleyways, under cover of darkness, and only when the man in question is desperate and judgement impaired. In the city, at least. In the country everyone pees when they have to, gender whatever.
Public defecation, though, I have no hesitation about shaming someone for unless it's some sort of emergency.