Nothing in the ISSF or the NSRA rules to stop you, but you could get more advantage by using shoes, as the advantage you feel from no shoes is caused by the ability to "use" your feet, spread your toes, etc. This is why for rifle shooting the boot should support fully the ankle but there should be space around the front of the foot and toes to let the foot work. With pistol you're not allowed a shoe over the ankle but a good fitting pistol shoe will give a little ankle support but should still be big enough in front to let the foot work. A good cheap pistol shoe made for the job is the Mannel (Harry Preston used to do them, he may still do) around £80 or the cheaper option is to use skateboard shoes, which are also made for standing still and controling.
Or if it works for you stick with no shoes!
Good Shooting