I would be surprised if it did as well monetarily standard index funds, though that would be rather beside the point. The set of companies in which a morally aligned index fund may invest is, by design, smaller than the set of companies in which an amoral index fund may invest, and so they may be intentionally passing over profitable companies.
One of my favorite quotations is from A Man for All Seasons, with Paul Scofield as Sir Thomas More. "If we lived in a state where virtue was profitable, common sense would make us saintly. But since we see that avarice, anger, pride and stupidity commonly profit far beyond charity, modesty, justice and thought, perhaps we must stand fast a little, even at the risk of being heroes."
Then if you have a big enough problem, forego the benefits of index funds.
A liberal, globalist politics really IS best for Google, Apple, Microsoft and many others, and thus it is correct for their leaders to say so. If you on the other hand dislike liberal globalism, then you have the choice to divest from/not profit from those companies. (Alternatively, you could invest in them as a kind of personal diversification.)
Why not? It would just mean getting out of those funds, and taking a hit putting your money somewhere less friendly to your wallet but more friendly to your ideology.
That's an opportunity for an ideology based index fund.
Of course, having said that...
I'm not sanguine about the relative performance of such an instrument.