This is identical to the problem with causal decision theory which goes “If determinism is true, I’m already certain to make my decision, so how can I worry about its causal impacts?”
The answer is that you swear the oath because you calculated what would happen if (by causal surgery) your decision procedure output something else. This calculation gets done regardless of determinism—it’s just how this decision procedure goes.
This is identical to the problem with causal decision theory which goes “If determinism is true, I’m already certain to make my decision, so how can I worry about its causal impacts?”
The answer is that you swear the oath because you calculated what would happen if (by causal surgery) your decision procedure output something else. This calculation gets done regardless of determinism—it’s just how this decision procedure goes.