Thumbs are incredibly necessary for most things we do with our hands. Shooting a pistol is not one of them.
When I say thumb in this context, what I am talking about are the two bones that make up your thumb (proximal and distal phalanges). There is no job for your thumbs to perform while shooting a pistol so try to keep them out of the way.
A common mistake that I see many people make in classes is leaving their firing hand thumb flat against the side of the gun and then gripping over the top of it with their support hand. If that meaty part of your palm (the first metacarpal, the hand bone your thumb is attached to) is not in direct contact with the gun, that hand is not doing much to support the gun.
Another common mistake, that is less detrimental but certainly optimal, is when the firing hand thumb is left parallel with the barrel along the side of the gun, and then the support hand grip ends under that thumb.
The above grip can be workable if your grip is strong, but you are making it harder on yourself if your grip looks like this. If you point your firing hand thumb at the sky, then regrip the support hand as high up as you can, your grip will be much more effective and it will make shooting and recoil management much easier.
In the photo below my support hand is up as high as I can get it, the meaty metacarpal pad is clamping down on the side of the gun, and my thumbs are completely relaxed and not applying pressure at all.
Depending on the pistol I am shooting, my thumbs may not even be in contact with the pistol at all. On any pistol I shoot, my firing hand thumb is resting relaxed on top of my support hand and is not touching the pistol at all. If I'm shooting a Glock, CZ, or most other pistols, my support hand thumb may be touching the frame, but it is not applying any pressure at all. When I shoot my Berettas, my support hand thumb floats off to the side also not in contact with the gun. This is predominantly because my thumb wants to come down right on the slide so I just float it off to the side.
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