Master of Puppets (MoP) makes no editions to any base game files or assets, it only adds its own code and assets, so it should have no issues with any other mod unless:

• Said mod adds items with the Row Name ranging 75620001 - 75620003. Well obvious conflict in this case, items will sure be missing;
  
  
• Changes the bonus growth values from the food items of followers diets. In this case your follower will most likely not receive the buffs from their diet food items but the other food items should keep functioning as intended;
  
  
• Customizes the Behavior Tree of thralls. In which case the Smart Weapon Throw setting will override the other mod customized behavior.

MoP should be compatible with all mods that increase the max level of thralls/pets.

Any other kind of supposed "conflict" is either a problem with your game files/PC (which I honestly don't care) or you are trying to add another mod that implements the same kind of functionality as MoP, in which case you will have to choose which one you want to use.