The Modrons have the following trait:
Axiomatic Mind. The [modron] can't be compelled to act in a manner contrary to its nature or its instructions.
What does this mean?
It sounds to me like nonphysical means fail to make it act in a contrary manner. It is pretty clear that persuasion and intimidation would never work in such a case and since I, as GM, decide on skill checks anyway, that is no problem.
But, does this mean that the modron is immune against spells such as suggestion? Or against the charmed and frightened conditions when they would ask for contrary actions?
Clarification: "spells like suggestion" means spells that can be used to force a course of action, also including mass suggestion, command and dominate monster.
Best Answer
It keeps the modrons from doing things contrary to their instructions
But instructions are not infallible!
In the general description of Modron's in the MM:
This puts a greater burden on the caster to make things like suggestion and command work.
An example would be if a a modron was told to guard a door. If this was a normal being you could suggest falling asleep, the door is moved, or so forth. But these would all be contrary to the instruction. It knows where the door is, it cannot move, it cannot be watched if the modron is asleep, etc.
But I could suggest, "Guard the door from the other side."
That is still well within the parameters of guarding the door. So it could still obey the suggestion by opening the door, walking through, and standing on the other side of the door.
Dominate Monster would work similarly. You cannot make them do anything contrary to their programming such as attacking another modron. However you could say, "That modron to the west of you has turned rogue. Subdue it so that it may be reprogrammed."
This means there should not be a blanket statement of "immunity to charmed and frightened". The caster just has to work harder to make it stick.