If you think you know me, you don't
If you think the solution to the riddle is something knowable and definite, you're incorrect, since the cat is inherently an unknown.
Settle arguments is my plight
The cat was a thought experiment intended to illustrate the ridiculousness of the Copenhagen interpretation, as part of discussion and debate between Schrödinger and Einstein. The cat is put into a deadly plight in order to settle the argument.
Tempted to see me? I'll likely die
While the box is closed, the cat exists in a superposition of life and death. However if you're tempted to see it and open the box, observation will lead to a definite probability of the cat being dead.
As it stands, this riddle has many answers
A reference to both the apparent ambiguity of the riddle and also the fact that all seem correct until the riddle is definitively solved, as if in a state of superposition.
Common of riddles, only one is right
However, on solving/opening the box, one solution is determined to be the real one.
"Only one" is in scare quotes, because though it's a single answer, it is also a superposition of two answers (an alive cat and a dead cat).
Schrödinger was certainly a brilliant mind, and the cat, being a thought experiment, was literally born of it.
The first letters of every line are STAC, or CATS backwards. (This relates to Hint 1, in that taking only one letter from all four lines spells out the answer.)