depends strongly on the POV I'd argue. I think I know what you mean: If you don't enforce equality by taking away freedoms naturally an inequality will emerge.

One could also argue that this desired freedom doesn't exist, because the moment you have that imbalance you automatically have a large group of people who suffer less freedom due to less wealth/power.

One might even argue that limitations can create freedoms. Because murder is usually a crime that is punishable by law, it is much easier to create non-violent business in modern, western countries. Few people would say that they are less free because murder is taken out of most people's equation.

I don't think that freedom and equality of opportunity exclude each other any more than freedom excludes itself. Frankly I would go one further and say that equality of opportunity is freedom, and that rules impinging on equality of opportunity is impinging on freedoms as well.

It is not a contradiction that freedom can exclude freedom. My freedom to own land excludes your freedom to do what you want with it, etc.