Some accused me of cheating. Is there any recourse?

The notion annoyed me to distraction. 

Can I block such messages in the future?

It would be great if there was an ignore feature.

Help explains how to block. However, there is no "ignore" feature. That's up to you. 

You can block users from messaging you, chatting, commenting in your threads. I think there is a limit.

The only way to stop everything is to block chat and to disallow notes on your profile. 

Most people put up with occasional problems because of all the good interactions that happen.

click "disable chat".

You can also put some tape on the screen where the chat stuff is.

If your not cheating, why worry. 

Sue the S.#.B.s.

Depends on whether you ARe cheating or not.

If not, your opponent is a sore loser. Laugh at him.