Dropout derailleur hanger straight - as in aligned perfectly parallel in the frame? You cannot really accurately tell by just looking. And even if the dropouts are parallel the hanger may be bent. This could effect shifting, especially when chain is under torque but not noticed when on a repair stand.

Park makes a simple tool which any bike shop should have. It just threads into the derailleur hanger and then you manually check the gauge at different points around the rear wheel rim to make sure the derailleur hanger is not bent fore-or-aft or down-or-up. If anything is tilting off, the gauge is then used as an alignment tool - just pushed or pulled gently - until everything is set just right. Takes all of about 5 minutes for someone to check and/or adjust anything.

... Also, even a "wobble" in an old worn freewheel could cause problems when shifting...

... Bent or worn derailleur or derailleur cage...

The Good news is that this issue is common and never a serious problem to remedy, whatever the cause. Those are Great bikes. They were also made to tackle heavy loads and this factor can always amplify any unseen wear issues on even less frequently ridden bikes. Just try making the simplest and least costly adjustments first.

Good Luck!