If we assume that both you and MLK were right, but that different policies better suit different conditions, then your proposal could maximize meritocratic effectiveness in an already-very-fair society, whereas MLK's way (the Voting Rights Act) provides a better minimum standard of human rights (similar to 1st and 2nd Amendment protections for people).
https://www.crmvet.org/info/lithome.htm#litbkgnd
Sorry for the snark, it's just a very hard problem because we'd end up in a situation where the voters would decide who is part of their club.
I've had this thought before and my tentative conclusion is "no". It boils down to the purpose of democracy which is NOT to produce the best government but to make people feel ok about having a government at all.
The idea has been around for a bit and I call it interesting, but also with huge potential of misuse.
Change the test slightly, so your target audience will yield better results, giving you a better result.
Either way, as long as climate change and darwinism are controversial topics, I see it hard to implement in a meaningful way.
Would it be a better system if the not-allowed group is totally dependent on the people that are allowed to vote?