Some seem to be; those aligned with secular values would necessarily be what you’d consider socially progressive, although once upon a time, they would simply be considered: regular.
They would _necessarily_ be socially progressive though.
Because they are public funded institutions. Public funding is a community effort. Community based systems are typically progressive in nature because they are at odds with notions of individualism or its extension of “family first”.
Some community based systems might not be: Religious institutions are community systems and if the communities are enclaves tied to a particular church membership, then you may find non progressive community based systems.
But if there’s more than a singular population in a community, the broadest cultural institutions will necessarily be socially progressive.
Preservation of Heritage for example, is a crucial function of cultural institutions.
a focus on Heritage is a progressive value when viewed from a broad perspective, but it can be conservative in its application.