Have just had a first time experience: never had problem accessing Priority lounges until yesterday in Portland (Oregon). The notice outside the Alaska Lounge said no room for Priority Club and another (paid) card. Had turned down a breakfast offer so this was slightly annoying. While waiting noticed the large number of entrants wearing shorts and yoga pants (see another thread) so getting status on Alaska must be easy!
Experience in SFO much better as when checking my seat assignment at the BA lounge was kindly offered entry despite not being qualified so cannot comment on the Air France lounge that is offered to Priority Pass.