The USSC did decide on the BSA's behalf that they are a private organization and therefore have the right to discriminate.
In this case (should it continue) the BSA is in the position of defending San Diego's lease of the land at a nominal rent. The city has bowed out and will not defend its own actions. I imagine the issue comes down to whether the city can lend its resources to a private (though benevolent) organization which discriminates.
San Diego has entry in its municipal code which might apply:
City Facilities. It shall be an unlawful service practice for any person to deny any individual the full and equal enjoyment of, or to place different terms and conditions on the availability of the use of any City facility on the basis (in whole or in part) of such individual?s sexual orientation or gender identity.I haven't seen the suit so I'm not sure what its basis is. There may be other city, state, or federal laws that could apply. I'm not sure that this is a case that'd make it all the way to the USSC. It does have relevance to dozens, maybe hundreds, of BSA leases and accomodations.