The reason some aircraft preclude turning as part of an RA is because of performance. The RA climb performance might be more marginal in some circumstances if the aircraft isn't turning.
But apart from that, in general terms, there is no inherent reason why you shouldn't be turning just
as long as you aren't doing so based on looking at your traffic display.
Still plenty of scope for non TCAS encounters, either by MEL or interaction with non equipped aircraft, so turning for collision avoidance should not be automatically labelled 'never do this'.
pb
p.s.
We all remember what happened last time an RA was ignored don't we?!
Well, we know what happened when a manoeuvre opposite the RA was flown, but that's something different.