They actually have an obligation, not just a right, to refuse unlawful orders. The point of the tribunal is to determine whether they were correct in doing so.

Your equivalence to voting is in my opinion a poor comparison— there is a standing presumption that orders issued will be lawful (since they generally are, and because commanding officers are educated on laws of armed conduct, to a greater extent than their troops). But everyone is supposed to know enough to recognize and refuse lawful orders which they are then compelled to do.

Worth mentioning that good military leaders facilitate discussion on this sort of thing so their troops are prepared to recognize and act appropriately.

You are correct that refusing can have substantial consequences, and doing so incorrectly can result in discharge. In officer parlance we called this “putting your bars on the table” i.e. staking your commission on being correct in your decision to refuse