I have a solution

Amazon obviously has a lot of money. Why won't they shoot several versions of the show with different casts?

Version 1: Nothing special. Everyone looks just like Tolkien envisioned and we have always imagined they should look.
Version 2: Diverse cast
Version 3: Diverse cast + LGBT
Version 4: Diverse cast of trans-people
Version 5: Diverse cast + LGBT + trans + socially relevant themes are explored. Elves discuss environmental issues, Dwarves have to overcome challenges of building a Socialist economy in Moria, Gondor is slammed for occupying the West Bank of river Anduin etc.

So on Prime you get to choose the version you want to see:
Version 1 watchers just get what they paid for.
Version 2 watchers get Prime free for one month
Version 3 watchers get Prime free for three months.
Version 4 watchers - half a year
Version 5 watchers - a year free Prime plus Amazon credit or something.

This way everyone is happy:
Fans can enjoy a proper adaptation of their favorite classic.
People who have no imagination can relate to characters who look just like them.
People who like free sh*t get their free sh*t.
You will be able to see Amazon's virtue signaling from space.

And activists will be happy. Or will they? Cause maybe they can't be happy unless they force people...