I guess whether you see equality depends on what type of equality you are looking for. If you are looking for equality of outcome or equality of opportunity via enforced baselining (such as very high tax rates or banning of private schools or healthcare) then you won't find them under liberal. If you are looking for equality of treatment then you will do.
The only thing I can say on this is that your examples, still, display a false dichotomy or understanding. Or willingness to openly, and rationally, discuss social and economic policy.