MBAM free doesn’t have any resident (on-access) protection, so there’s no problem. I’ve never used MBAM Pro, so can’t comment from personal experience, but others here say that one’s no problem either.
When I run an MBAM on-demand scan, typically a quick scan once a week, I’m in the habit of temporarily turning off avast’s file shield first, which speeds up the MBAM scan a little since that way the two aren’t to some extent scanning the same things at the same time.