How do you expect to achieve even equality of opportunity when those differences exist?

First, you don't need to achieve exact equality, just approximate equality. That approximate equality can incorporate a range of levels of wealth and still be enormously more equal than what we have today. It is fine if someone with an IQ of 130 has 100x the wealth of someone with IQ 70. It's not fine if someone with an IQ of 130 has 10^9x the wealth of someone with IQ 70. It's also not fine if someone with IQ 130 has 10^9x the wealth of someone else with IQ 130. (It's questionable whether IQ is even a meaningful measure, but I'm just using it here as a proxy for whatever kind of "innate ability" we want to posit.)

Second, you don't need to achieve equality of all forms of outcomes, just economic means (and political rights, etc.). Not everyone can be a concert pianist or a venture capitalist, but that's okay as long as concert pianists and venture capitalists don't have 1000x the wealth of everyone else.

It's perfectly fine for people to have different aptitude and even different levels of aptitude in general. It's just not fine for those differences to translate into enormous differences in baseline well-being (e.g., food, shelter, time).

Ironically, of course, if we achieved this, it would then be much less objectionable for Stanford to do whatever it wants, because it would mean we've created a society where going to Stanford doesn't really matter so much. But the question is what does Stanford (and everybody else) need to do in the meantime to get to that point.

Equality of opportunity is relatively easy: you provide people with the same opportunities, that they must meet at their own innate capacity and motivation.

I don’t defend that a doctor should make 20x what a nurse does, or that the c-suite should make 20000x what the janitor makes. But it’s also fine that some people don’t produce anything of value, at all, while others produce a lot of value for society. A meritocracy with a mechanism to limit suffering and harm to those who cannot participate seems a reasonable solution. We don’t need or want to incentivise parasitism at high or low levels.