Yes. I'm either in a conflict zone and I've selected my 'side' or I'm engaging a pirate target. The hitting with a non-turret weapon used to work, but not anymore: since Sep update patch 2, I think.
Hmm, does sound like a bug then.
The only other thing it might be, is that beam turrets seem to be the slowest to swing around and get on target, so if you are up against nimble opponents, it can seem like they are not doing anything. On my turreted Krait Mk2 I try to "help" the turrets by keeping the enemy roughly in front of me and turning with them so the turrets don't have to do any extreme targeting corrections (since I'm using beam turrets too and they are slow to get on target).
You could try some tricks like replacing the turrets in outfitting and then putting them back, or swapping them (if they are the same size) around to see if that shakes something loose. I haven't noticed any turret issues on my Krait, but it might be a setup-specific thing for you and changing stuff up might force the system to "recalibrate" whatever the error is.