Hi chessrookie321,
This may happen the odd time, but yes there are precautions you can take.
First of all, you could try play more people that you know.
If you dont want to do that then , you can do as you were doing and disable the chat.
After you disable the chat you can , click their name and click "Block", this will stop them contacting you post match or sending a message to you.
Also it will ensure you dont play them again when you put out a seek.
If they say anything abusive, you can copy and paste the chat and send a report to staff here:
http://support.chess.com/Tickets/Submit
Regards
Hydra
Recently I been playing some live chess standard and most of the people I play have been spamming the draw button when the person was losing lately. I keep refusing them so the opponent gets the picture that I am not accepting their draw but they keep doing it. And when I try to ignore them, some of the people say something like why i am not accepting it and wont stop. Then I disabled chat sometime and a couple people leave a message in my box saying how I disable the chat and everything. Is there a better way I can deal with this?