Using FMJ on game can be tricky, meaning your round will fly right through your target and transfer very little of it's kinetic energy into the animal. Hollow points and soft points are the best for hunting because they mushroom out or crush which transfer most of thier kinetic energy to your target. A headshot or heartshot is best when using FMJ's.
Saying this, I still use FMJ when I hunt coyotes with my AR because I can't afford to buy the expensive hunting loads, I just aim for the head or heart.
I would assume that the reason your state has banned the use of FMJ's for deer is because once fired they will go a long way and if your state flat, there is no hills to stop them. In Indiana we can't use high powered rifles for deer for this reason, most of Indiana (with the exception of the southern region were I live) is like the great plains and if you miss, your round goes a long way. Because of this we have to use shotguns.
Century Arms AR-15A2, 5.56
1946 Mosin-Nagant M44, 7.62x54R
1978 YUGO SKS, 7.62x39
NEF Protector Pump, 12 gauge
Savage Model 64, .22LR
NEF Pardner Tracker II, 12 gauge
Rock Island Armory 1911A1, .45 ACP
Remington 870 'Express Magnum' 12 gauge
Bersa Thunder .380