If you want to be competitive in autocross as a priority, lose the flywheel and build for ES or STS.
If you want to build the car how you want, build the car how you want and autocross wherever it ends up. You can still compare times with people with similar cars, compare your driving improvements over the season relative to the fast guys, etc.
And as someone said, if you have a mildly prepped car plus a flywheel, no one will care at the local level. If you have a FULLY prepped car plus a flywheel, IMO that's cheating.
This is a generalization to give you an idea of the progression through classes:
ES - Shocks, 1 sway bar, cat-back exhaust, stock width rims with 200 TW tires
ST (STS with an open diff, STR with a Torsen) - ES plus: springs (coilovers), any sway bars, 7.5" wide wheels, CAI, Header, hi-flow cat, certain tuning options, seats, steering wheel.
CSP - STS plus: engine swaps with certain years, update/backdate of various parts from other year Miatas, very wide wheels, DOT R-compound tires (Hoosiers), flywheel, clutch, diff, aero, ignition, and more.
SSM: Money. Spend a whole lot of money. On everything.