I think it could be
My prefix isn't a great date.
LI - lithium acts on the central nervous system to stabilize mood, while this is great for someone bipolar or manic, it could be seen as making an average person boring, and at least not a great date (no excitement, but not bad). It can be associated to mythical hate as people suffering from such illnesses can often hate things or others without reason/anything based in reality (mythical), and it's a common treatment for them.
My suffix is a great gate.
OR - see @LukasRotter 's answer for explanation
My infix helps keep order.
quo - quid for quo keeps order, or maintaining the status quo
My whole is a disorder.
Liquor - while note directly a disorder, liquor/alcohol abuse is a common disorder in many parts of the world.
Maybe a stretch, but best I could come up with |\('.')/| <-- attempted ascii shrug