Equality of opportunity is a universal humanist tenet. We want all groups to have equal opportunity to flourish and pursue happiness. The concept is politicized by the right more than the left, but only as opposition to equality of outcome.
Equalization of outcome is a central tenet of all progressive societies. Equality of outcome is a leftist principle, but equalization through progressive income taxes and other means has indisputable economic benefits since we each need a single home, bugati, and smart phone, and we each have limited food and beer intake capacity. The more people able to afford life's needs the more we can occupy people in producing them.
Equality of responsibility is a central tenet of business, partnerships and cooperatives. Each partner is equally responsible for the organizations financial obligations/expenses while sharing in profits/revenues. This has been ignored as a social/political organization tenet.
In a social context, equality of responsibility is actualized by replacing some taxation with user fees. One way that doesn't compromise equal access to services such as education and healthcare, is to offer loans at subsidized interest rates to patients and pupils to pay for their use of those services. A hybrid approach that considers the 3 above equalities can involve socialized subsidies for licensed and regulated price controlled services along side private alternatives that can still tap into socially subsidized user loans for services.
The above proposal tends to significantly reduce the need for taxation, as services are paid directly by users, and tends to lower the cost of social services because of the need to provide customer value. For the rich, advantages of lower taxation are offset by actually paying off loans or direct services. For the chronically poor or disabled, there is little change, as they get continued access to services while being unable to repay loans. For the successful poor (those who gain future benefits of income and life from education and healthcare), the disadvantage of having to actually pay for their services eventually, is offset by not having to pay (through progressive taxation) for other people's future services after they achieve their successes.
This is the first step in modeling society as a cooperative enterprise where equal members are also consumers of the enterprise. You can imagine multiple cooperatives side by side with different philosophical commitments and support for its members, as well as missions for the organization. Membership is transferable and members can sell out of one and buy into a new cooperative society.
Egalitarian cooperatives self-enforce the principle of association, and is the only political organization that can prevent development of hierarchy and its oppression. Though limiting power limits the speed and decisiveness of action, it more importantly limits corruption.
The principle of association states that a group of equal free people voluntarily associating into an organization would not cede their right to divorce from the association, or a means to recall an elected administrator. They would not grant their administrator rights to disposess them of their property or risk their human rights through war or other protections of the administratorship.