Company management has fiduciary duties to all shareholders, not just the majority.

In theory yes, but in practical terms taking care of board members and few remaining big shareholders is enough.

'In practical terms', the other shareholders can still sue you.

It seems to me that this is extremely unlikely to be true under corporate law. Do you have a reference? In particular, there is no unique group or shareholders that makes the majority!

Even if the law or corporate statute requires that owners of, say, 10% of shares should be able to raise the concern or even block big decisions like a sale of the company, in practice the ownership is very uneven. Just 10% of owners can own 90% of shares.

For less drastic decisions where holders of 50%+1 or 2/3 of shares is enough agreement of board members and few more shareholders is often enough.

And even with less skewed share distribution views of shareholders are very broad and the board does not have troubles to form the necessary majority.

Surely shareholders coups are possible, but those are rare.