OP, pretty sure you are using the tool below. I use it also. If the scope rings are not dead nuts on top of the receiver and you have to tilt the stock left or right to get the scope bell perfectly over the barrel, then the stock itself is not straight on your shoulder or palm of your hand and you tend to tilt the rifle so the stock is correct.
If that is happening, don't use the tool, just level the stock to your world and then align the crosshairs to a plum bob, like mentioned above and it will probably resolve the issue.
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Yes that is the tool that I am using. I will try what you have suggested.