It's a great point. I think we should definitely have a conversation about this, although I'm not necessarily sure I have useful practical ideas. I do have something that may be an unpopular argument though.
It's that the way ahead simply related to personal responsibility.
We should have the right to express feelings in the workplace and technically we do, save for that fear of judgement. I do think that judging is a normal, human thing to do. It's when judgements start have additional repercussions beyond their simple existence that brings trouble.
"Look, he's crying, he can't handle his shit" is a fair point. You can't handle something so it's coming out and it's a form of expression and it's fine. It's ok to let it out and it's ok for others to think whatever. If someone has the right to express something, there shouldn't be an implicit condition to stop others from expressing their reactions. But if it turns into "he can't handle his shit so I don't want to work with/be around him" that's the bad thing. People do human things and for sure we shouldn't make them feel they shouldn't.
We should be able to express our feelings but we should also own the responsibility of the effect it has on others.
You're in the workplace, doing your work stuff, you're in the flow of productivity and suddenly someone starts crying. There are people in the office, in various stages of activity. What do you do? You might stop to provide acknowledgement and build up some resentment about how the other person decided to do this in the open and place this burden of reacting on everyone else. Selfish. You might feel the pressure to act, lest you be the target of judgement. (Look at him, someone's crying next to him but he can't be bothered to ask what's wrong). You might simply become victim to the crowd responsibility (someone else will react).
Everyone reacts differently since we're all different and someone crying is a sign of distress that we as a society are primed to react to. If I want to unload, is it fair for me to provoke reactions in everyone around me (curse those open spaces) because I'm having a moment of emotional unloading (hey, please acknowledge me!).
I don't think there's a one-size-fits-all principle. Situations are different and the action to take will be different: someone it may be ok to unload in "public" (more or less), other times it may be better to withdraw to a more private-ish space.