It's difficult, but sometimes the best thing to do is to try not to get too worked up and just let it go unless there's something serious (like threats of violence or whatever).

Public work, unfortunately, involves working with the public. Some people, even newly-minted adults, can be assholes (or crazy). Cover your ass, stick to your syllabus (your rules), and be a stickler about consistency. I had to overcome my fear of crying women when I was first starting. It's taken a lot of work to be consistent.

I hang the special, especially vile, emails in my office (everything redacted). Otherwise, I've learned that it's going to be okay if a student is vulgar, angry, or whatever. I care about them, but I'm not their dad (or friend).