I was right. You do not need membership card to gain entry to the Alexander Sauna. Below is a comment from one customer:

ALEXANDER SAUNA autumn/autunno 2017

“Due to an old tradition of gay hospitality 80ties this ambiance was favorite from married men and others who rescued anonimously did not need a card of admission.

To day after to different ownership we have a terrible decrease of hygiene, safety and people in the club. It is almost hard top approach other men for the arrogance of hustlers, who run after you, willing small money (10 Euros) just to leave you alone without annoying. I think this is bad and irresponsible in charge to someone who run a public/gay/sauna“