Not GP, but I don't care if a random person does it. I care when someone who is, ostensibly, intending to interact with me does it. You can't actually tell whether they're engaging with you fully or not, like if I were conversing with someone (in person) and started typing this comment at the same time.

You never know if the person you're interacting is actually listening to something and distracted or not.

Remember when I used to go to the office and I had to guess whether my colleagues were on a call, listening to music or "available" because there was no way to know from the outside since they never removed them.