I had nothing but trouble when running both as resident.
In fact it was here on the forums that it was recommended
to not run both because of conflicts.
I don't see where or who recommended not running SAS and Avast as resident as they aren't both antivirus programs. Unless you are changing your original point to not running SAS Pro with avast to running two resident anti-spy/malware applications.
So there would be no difference on recommending SAS or MBAM to run alongside avast. The only proviso would be not running SAS Pro and MBAM Pro as resident and that has nothing to do with avast, but running two resident programs of the same type (2 X anti-spy/malware or 2 X antivirus).
I had SAS Pro before MBAM came out and for some time I had SAS Pro as the Resident and when MBAM came out I had that as the free version non-resident along side SAS Pro.
When I bought MBAM Pro, I switched SAS Pro to non-resident alongside avast and no issues at all in all of the years I used SAS Pro - I ended up uninstalling SAS Pro because it didn't bring much else to the party (MBAM Pro and avast).
There should be a point when you review what security applications you have installed, effectively when you spend time servicing those applications rather than they serve you, then you don't have the balance right.