Sec. 91.307 — Parachutes and parachuting.
(c) Unless each occupant of the aircraft is wearing an approved parachute, no pilot of a civil aircraft carrying any person (other than a crewmember) may execute any intentional maneuver that exceeds—
(1) A bank of 60 degrees relative to the horizon; or
(2) A nose-up or nose-down attitude of 30 degrees relative to the horizon.
It's not a matter of whether spins are aerobatics or not, because the regs say nothing about parachutes being required for aerobatics, or whether spins are aerobatics. The regs specifically define aerobatic flight, but the chute requirement simply has to do with max. pitch and roll attitudes as described above. Spins certainly exceed both. Lots of folks seem to think that "aerobatic flight" starts when an airplane exceeds 60 degrees of bank or 30 degrees of pitch. It doesn't, and it's not part of the Feds' definition of aerobatics - it's simpy the criteria for when chutes must be worn.
No chute requirement when solo, regardless of how you're flying the airplane.
Per FAR 91.303, aerobatic flight is simply:
an intentional maneuver involving an abrupt change in an aircraft's attitude, an abnormal attitude, or abnormal acceleration, not necessary for normal flight. And we all know that can be pretty much anything. Is an intentional spin necessary for normal flight? Does it involve an abrubt change in attitude? I'd say so. And who defines what's "abnormal"? That's latitude for the Feds to bust your ass if they really want.
But again, whether or not spins are technically "aerobatics" makes no difference when it comes to the parachute issue.