The concept of Equality, in the US, at least originally, meant that all humans, by virtue of birth, had the same Rights, and the same ability to exercise those Rights. It did not ever mean or imply that everyone should have the same health care, education, wealth, housing, social status, sexual orientation, etc.
What it's supposed to mean is that all should be equal under the law, and that all have the same inherent Rights, which they may or may not choose to exercise.