They're specifically not supposed to represent the interests of a minority of the shareholders!

That doesn't mean they're required to faithfully represent the interests of any one person with majority voting power, but it does mean they can't select some random subset of minority voters and serve them instead.

Legally the board has the duty to represent all shareholders, minority and majority, and of they cannot they have to resign.

I didn’t say that they’re beholden to the minority, they have a duty to ALL shareholders which is generally most clearly expressed through acting in the wellbeing of the company itself.