My point above is that the ABA is the same kind of thing as the Federalist Society. They’re both private organizations. The ABA isn’t some sort of quasi-public body.

The fact that the Texas Supreme Court previously relied on the ABA’s list of accredited schools doesn’t change what kind of thing the ABA is. In CS terms, the Texas Supreme Court rules just had a pointer to the ABA list. That doesn’t change the nature of the object to which it points.