You take the test twice, once with a blindfold on, and once without a blindfold. As an objective measure of your intelligence, I expect you to get the same results on both tests

You are considering whether it's objective only by that the reader at the end sees the final score, but there's many spots in between an empty sheet of paper and that score where somebody's subjective experience comes into play

We can argue about whether or not the stuff on the test is important. We can discuss the various environmental, cultural, and socioeconomic factors that go into the kids taking it and how that impacts scores statistically. We can even talk about the various medical and neurological factors that go into test taking generally and standardized test taking specifically that can affect some people more than others. I'll even concede that the SAT/ACT isn't a test of your intelligence so much as it is a test of how well you did on the SAT/ACT, just like putting things on a scale may at best be a measure of its weight relative to other things on that specific scale.

But at the end of the day, more right answers === a higher score, and I'm not sure how you get any more objective than that when it comes to something as fluid as academic ability.

Getting rid of one of these because it's easier if you have money (when all of these things are easier if you have money, because life is easier if you have money) is just setting the stage for more explicit bias.