In my opinion this claim seems completely logical. It came to my mind after seeing the fez hat that Stan is wearing similar to the ones that the Shiners (a freemason organization) are wearing. Also in the Mystery Shack Mystery game in the living room there is a hanged rug on the wall titled "The Royal Order of the Holy Mackerel" which seems like a name that a mason body organization would have, also its symbol is similar to the symbol of the Shriners. The show is also using clear symbols used also by the Freemason society most importantly the "all seing eye" or the "Eye of Providence" (Bill Cipher). In a number of episode segments we can see the secretive mysterious side of Stan, that in aspect of popular culture is all that being a Freemason is. I think my judgement would eventually reveale itself in the following episodes of the show.