Years ago there was a lot of controversy about the alleged lack of accuracy with an autoloader, that was largely a myth. Like most things firearms related, many folk distrust and even dislike new things and find reasons to do so, even to making up and perpetuating rumors.
Look at the way each action works, the bolt pushes the round into the chamber, then rotates and locks, this is the same with both action types. When the round is fired, the bolt rotates to unlock, then is pulled back extracting and ejecting the spent case. The only differance is the motive force involved, eithr gas pressure or manual force, the effect is the same. The force involved to work the mechanics of the action, has nothing to do with accuracy. That is intrinsic to the shooter and the firearm itself.
Now that is with a centerfire chambered long arm, handguns and rimfirea are mainly blowback actions and a that is a differant kettle of fish