Deal with the annoyance. Turn your volume down.
Willingly preventing a teammate from communicating with you and vice-versa puts you at a disadvantage regardless of how you look at it. In all walks of life, you will have to deal with people who you find unpleasant. Strap on your big-boy belt, be straightforward that the shortcomings of your team can be attributed to the bad choices of the players in question, and play on.
You don't even have to make small-chat with them (gasp!) outside of team-coordination stuff, but coordination wins games. So don't go muting people. And certainly don't go around making threads to make pings even more irrelevant in the places that most need them.