The short range target used in F-Class uses a .4MOA V-Bull and a .8 MOA "5" ring". If you want to succeed and be competitive, you need a .4 MOA gun or better. Most semi-serious F-Class shooters are shooting .2-.3MOA capable guns.
2 minute rifles would not even come close.
For medium and long range, the target is a .5 MOA "V-Bull" and a 1MOA 5-ring. In order to be competitive you need a gun that is a minimum .5 MOA performer at long range.
The reality is, an accurate gun teaches you to be a more accurate shooter. Even bargain basement Mossberg Night Train rifles at $450 will give you 2 MOA performance with factory ammo. Becoming a good long range shooter requires mastery of the rifle, the ammo and the conditions. Nobody can go on a car lot and buy a car that will win a Formula 1 race, nobody can go into a wholesale sports and buy everything they need to win a semi-serious F-Class match either. There is more to shooting accurately than just the gun.