Actually, no
I know what you are saying but you are wrong.
America in no way was founded on equality, of any sorts.
It was founded on Liberty, which means equal opportunity and is significantly different.
The defining trait between the left and right in America is around Liberty.
The left interrupts Liberty as making laws that force equal opportunity.
The right interrupts Liberty as making laws that prevent unequal opportunity.
The Republican and Democrat parties fall somewhere in the middle of those two philosophies.