The higher up the ratings ladder you climb, the more you're going to encounter obsessive chess players. And obsessive players tend to take their wins/losses more personally than your average, non-serious players.
Best bet? Just disable your chat. Who needs to chat during a chess game, anyway?
I believe you can also disable the option for others to leave messages on your profile page, as well.
What should I do if another member is rude or abusive?:
https://support.chess.com/customer/portal/articles/1444877