Is it possible leave Match Chat? I'm only interested in using voice/text with my own team. I glanced at the options menu, but I didn't see anything obvious.
Yes. During a match, press P to bring up channel settings. Click on the filled speech bubble next to "Match" to remove yourself from match chat. You can also remove yourself from team chat or voice chat in a similar fashion.
The settings will persist across matches, so you don't have to do this every time.
You can also press Ctrl+Shift+C to hide the chat. It also persists for the entire session.
To show the chat again either press Ctrl+Shift+C again or Enter.