It's a valid stance for a random individual, but not for a board member, who assumes additional obligations that are external to their own personal morals. If your morality and your board duties conflict, your obligation is to resign.
I think noisy resignation is the rational move for various reasons.
But I don’t think it’s required. The director under Delaware law is not conceptualized as a proxy for the whims of a majority of the voting rights.
Incorrect. Resignation is merely one of your infinite valid options. Your obligations are mostly not to do various incorrect things, not to do any particular specific thing other than pursue a goal.