The non-uniform forces, in this case, are the reaction forces at the supports.
They must be greater in order for the beam to be stationary in the accelerating frame.
i.e. the reaction forces are proportional to the weight which is proportional to the strength of gravity.
Presumably I can also make the stresses change by changing the position of the supports.
However, we usually try to change only one thing at a time in experiments.So - I have shown that objects
can experience stress under locally uniform gravitational fields, and that the amount of stress depends (amongst other things) on the local strength of gravity.
Generally, objects are not uniformly supported throughout their structure - so
So I have successfully shown you what I meant when I said
Depends on the circumstances ... high accelerations generally put a lot of stress on macroscopic objects.
(emph added)
You appear to agree, so I don't understand your objection.
Is it merely that you wanted to point out that there are other factors in play besides the acceleration?(Note: the "all other things" that remain the same, which you found "self-contradictory", referred to the description of the thought-experiment setup - keep that the same, change the gravity, then the reaction forces are different, the beam bending is different, there will also be some compression in the supports etc.)