Nystul's Magic Aura can make it so that magic and spells treat a creature as though it were another creature type. However the extent of this effect is ambiguous.
At first, it says the following, which specifically mentions spells which "detect creature types". One could argue that this means it only affects information gathering spells.
You change the way the target appears to spells and magical effects that detect creature types, such as a paladin's Divine Sense or the trigger of a symbol spell.
Then it goes on to give a far more general rule:
You choose a creature type and other spells and magical effects treat the target as if it were a creature of that type or of that alignment.
One could use this to change one's effective creature type to something like Dragon or Celestial. This would seem to make you immune to spells that require a humanoid target, such as Dominate Person, as well as magical monster abilities which require a humanoid target, such as the Vampire's Charm ability.
One could argue that Nystul's Magic Aura is intended to only fool spells which gather information, but one could also argue that any spell which only works on a specific creature type is one which gathers information, even if that is not its primary purpose.
Which is right? Would Nystul's Magic Aura make you immune to Dominate Person?
Best Answer
No, it would not.
The first part of the description clearly says "so that divination spells reveal false information about it." This then applies to both of the more specific uses (false aura and mask). Of course, a symbol spell is not a divination, but as you point out it still fits the "passive detection" pattern. This is indeed a RAW loophole that requires DM judgement to fill, the inclusion of the symbol example makes the exact scope not tightly defined.
In any event, allowing a second level spell to really change your type as far as spells are concerned is super powerful and abusable. "I'm type construct now, does cloudkill not work on me?" Therefore I think it's better kept tightly construed - you could fool a caster into not hitting you with the dominate person, but the dominate would work if they did.