The age a car has to be to not have to wear a seatbelt is at least a car made before the year 1966.
Basically a car has to be 54 years old or older as of now or any antique car that was not made with seatbelts where you do not have to legally have seatbelts installed or wear seatbelts.
If you have an older car and have anyone under 18 then they cannot legally ride in the antique car unless it's at a car show.
If you have kids under 18 then you must install seatbelts for them and use proper child restraints.
But as long as the car was never equipped with seatbelts then the car is exempt from seatbelts for adults or anyone 18 or older.
But kids must still use child car seat restraints or seatbelts depending on the child's age.