By RAW it’s unclear but I would say that it wouldn’t work
Note: My answer is specifically about Shield Guardian since that’s the creature the title of the question references, it does not apply to other minion creatures because they all have individual traits that affect their behaviour and should be considered separately.
As already stated, Shield Guardian has intelligence of 7. It’s not great but it’s not terrible either, I’ve had PCs with that score in my games. It’s probably enough for the Shield Guardian to understand a somewhat complex instruction but the reason why it probably wouldn’t work is not its lack of intelligence.
A Shield Guardian is a construct that is created with a singular purpose - to protect its master. Its entry in MM states:
A shield guardian's solitary focus is to protect the amulet's wearer.
The control over a Shield Guardian is tied to the amulet that’s linked to it, there can only be one at a time and if it’s ever destroyed, the Guardian is incapacitated (MM, 271). This suggests quite strongly that the Shield Guardian will only obey the single person who owns the amulet.
Moreover, there is not indication that the control its master has over the Shield Guardian is absolute. In fact, MM goes on to define two very specific things that you can command your Shield Guardian to do - attack an enemy or protect you from an attack. This suggest that it’s not a “general purpose” servant that will make you breakfast, fetch things for you, carry your backpack and so on - its only purpose in “life” is the protection of its owner from harm. Its description hints that it has some autonomy to choose how to best protect you, this is supported by its Intelligence score - it’s not a mindless construct, it can make decisions by itself.
Because of those reasons, I don’t think it could be ordered to obey other party members, it’s a creature with a very well defined, single purpose, that I think would not follow commands which either go against, or even don’t directly contribute to fulfilling that purpose.