Why are the A300/310’s electric pitch trim switches inhibited with the autopilot engaged?
Like with two human pilots, you want control1 to be explicitly in one hands. With autopilot, it's the same: it should be either autopilot or you.

In the case of 'breaching' the normal transfer protocol for whatever reason ("I have control" - "You have control", which in case of autopilot would be the autopilot disconnect button), there are two possible courses of action when the pilot just starts to control the aircraft:


Immediately give control by explicitly disconnecting the autopilot.
Keep control by ignoring/overriding the pilot as much as possible.


Apparently, Airbus espoused the second strategy. It made sense for them to ignore the pilot (whether for trim or main control) until s/he explicitly requests control. (There is not much the aircraft can do when the pilot starts to trim the wheel manually, so it still disconnects).

If the trim switches were not ignored, there could be two options.


Disconnect the autopilot. But this changes the whole ideology, and other things would need to be changed to be consistent.
Just change the trim. But the autopilot (which is still in control) would have to fight against it in order to keep doing its job (e.g. flying level), either by trim or elevator.2 This makes no sense and creates dangerous confusion.


Arguably, completely ignoring the pilot is not a very good idea, so Airbus had to change the algorithm at least in some situations.



1 By 'control' I mean guidance control, excluding things like stability augmentation systems.

2 Unless this is a simple autopilot which does not actuate trim at all and may then need help from the pilot. This is the case for some GA aircraft, but not for A300/310.