If passing one person the trail playing audible music ruins your entire experience I'd check on your mental health. Seriously. I too can get mad at ridiculous things (line cutters, rude drivers, loud movie goers) and have to make a conscious effort to stop, take a deep breath and ask myself why I'm letting this innocuous thing effect my day.

Imagine the scenario where you end up hiking within earshot and in the same direction as another group.

Tip: Take a small break and within 60 seconds you'll be out of earshot. Also, I realize we're not going to agree on this and that's okay.

The same thing works for terrible drivers on the road, pushy customers at the supermarket, and all kinds of other bothersome interpersonal situations.

They can be optional. Just grant yourself a moment to let them go away.

Out of sight, out of mind.

Isn’t it unlikely that both groups share the same hiking speed for a while? And even if you have the same speed, take a break or pass them quickly.