In mainstream discourse in the US, "equality of opportunity" is taken as an uncontroversial rallying cry for both "conservatives" and "modern liberals." It's typically seen as a more reasonable alternative to the openly socialist "equality of results."
Don Watkins, of the blog, LaissezFaire, has written two posts exposing the fact that "equality of opportunity," taken literally, is just as irrational and unjust a notion as "equality of results." (If it's not taken literally, then it's an extremely vague term and shouldn't be used.)
What matters for the justice of a society is not "equality of opportunity" but the absence of initiated coercion.
Just Say "No" to Equality of Opportunity
Who Needs Opportunity?
On Fairness and Justice: Their Meanings, Scopes, and How They Are Not the Same
How to Show That Taxation is Robbery
QuickPoint 2: Altruism Supports Coercion...