Now I understand you don’t want to engage with the angry person who is swearing over there. You can see that they’re upset, but you’re not entirely sure why, and you’re certainly not sure why they’re this angry. Surely such a little thing shouldn’t provoke such strong emotions in someone – they must be unhinged, or overly sensitive – surely.
After all, dealing with angry, upset, and/or sweary people isn’t pleasant and it certainly isn’t fun. So of course the logical response is to tell them to calm down, to tell them that you won’t engage with them when they’re like this, that you feel threatened by their response, and that their language is inappropriate and that they need to be more civil.
How about instead of telling someone how they should react to something, you think a bit about why they might be reacting that way, how constant microaggressions might have worn them down, and how this might have been the final straw after they’ve been polite to everyone else whose pushed them down that day/week/month/year. Think about how they might actually see the thing that you said or wrote, and how that might look from their position. Actually apologise for upsetting them and then invite them to tell you what you can do to avoid upsetting them again in future – because people generally want to avoid having their feet stepped on, they will often provide you with suggestions resources on how your organisation or yourself can be more inclusive, open, and less upsetting.
But if they don’t, because it is not their job to educate you, go and find those resources yourself. Read up on the issues, reactions, things to avoid doing, things to do, and ways to be a better person and organisation. There are many of people out there who blog about these issues, and you can read those and learn why it is that people are upset about this issue, and decide how you can be a better person/organisation.
If you still don’t understand the issues, go and talk to people you know who identify with the person who was upset and ask for their advice. Go and talk to organisations that represent the person who was upset and find out what you can do in future to avoid upsetting people who identify with that group. Be empathic, care about those who are in pain, and do what you can to avoid adding to the burdens they carry. Be a place of safety, sanctity and refuge from the rest of the places that haven’t yet learnt to be empathetic and better.
This is why I don’t follow certain famous people on Facebook and Tumblr anymore. Every time they screw up (and come on, everyone screws up), they complain about the tone of the people complaining, and threaten not to change/apologise if they don’t have people ask them to change/apologise with adequate politeness. It’s disgusting.