On a modern Aircraft like the A320 or B737, is it possible to disable computer interference with the control inputs of the pilots? One more question due to the recent and unfortunate events in the case of the second ever B737 Max 8 crash.

As far as I know, the first of the two crashes was caused by the MCAS System, that overwrite the inputs of the pilots as a faulty reading of an angle of attack sensor indicated a stall (that was not actually happening).

Knowing (rather, having an idea of) what a difficult time pilots have in such situations I wonder if it is at all possible to stop the aircraft from executing such maneuvers.

I know that on an Airbus A320, there is different flight laws. While during "Normal Law" all the various protections the A320 has are active (Stall protection, overspeed protection, bank protection with all their proper names and so on), they are not active in "Direct Law". There are two more levels between "Normal" and "Direct" (namely "Alternate" and "Abnormal Alternate"), but let's ignore them for this question.

I have never flown an A320 in real life and lack the training any A320 pilot goes through, but in the Simulators I have flown (not talking FSX here!) you could "exit" out of "Normal Law" by turning off the flight computers on the overhead, like the ELAC, FAC and SEC, and go into alternate or even "Direct Law".

So the question is: is this actually possible on a real A320 as well? And is there a similar method on a B737 (Max 8)?
For A320 it is possible also in the real aircraft. The problem with disabling flight control computers is that it also disables associated control surfaces. If you disable all five computers, you disable all surfaces and the aircraft goes in to "Mechanical backup" mode, which leaves pilot only the control of the trimmable horizontal stabilizer (ie. pitch trim) and rudder. Wide bodies are similar, although they have more redundant flight control computer architecture.

The correct procedure to override normal law in Airbuses is to switch two ADRs off, which forces controls to alternate law. This disables most of the protections leaving only load factor protection. All control surfaces would still be operating with automatic pitch trim. This would be used only in undue protection activation.