I know this isn't new to many, but it doesn't get said enough. Various conservatives and neoliberals get away with saying "I'm for greater equality of opportunity, meritocracy, but not enforced greater equality."
They should be called out on it, as it is utter nonsense. You cannot promote equality of opportunity without some amount of greater equality. Some kind of economic wealth redistribution is required.
Take education, the favourite go-to issue of "equality-opportunists" - you say you want to ensure low income people are able to attend good or even elite schools. Well Harvard isn't cheap. If someone too poor to pay its outrageous tuition is going to attend, who is going to pay for that? Whether you favour tax funded programs or private scholarships, you still require rich people to pony up cash and pay for low income kids to get into Harvard. Even if you're just talking about improving schools in poor areas, you need funds to make good schools, and if the tax base of the poor area doesn't support that, the money has to come from wealthier people.
Even legalistic means like anti-discrimination laws are a form of redistribution. Government has to pay regulators and courts to enforce these laws, and provide disadvantaged groups opportunities to have redress that aren't paid for by the taxes of those disadvantaged groups.
Capitalism generally distributes economic opportunity according to wealth or income. Rich people have more opportunity than middle income, who have more opportunity than low income. Yes, Albert Einstein born to a poor family will likely succeed in at least escaping poverty and possibly more, but dullards born to the wealthy will succeed and mediocre kids of the middle most often do too.
If you are really for greater equality of opportunity, you are by definition in favour of greater equality. If you're not, whatever ideas you have will fail and you're frankly most likely insincere about the equality of opportunity thing to begin with.