I'd like to be able to invest in an "index minus certain companies which I choose" fund so that people can exclude companies that they don't like for whatever reason.

You can. A bunch of companies offer SMAs like this. It's a retail product, usually labeled as some smart tax loss harvesting atop the indices where you can denylist particular stocks.

Fidelity offers one: https://www.fidelity.com/managed-accounts/separately-managed...

It'd probably take you an afternoon worth of time to research then enact it.