To start off, in Large Theme Games it is allowed to have exactly 2 different Mafia factions.[1] What this means is that you are allowed to have 2 scum factions which are both fully equipped to win.
A mason, adhering to the Normal Requirements, is defined as the following:
[2]A Mason group is a set of players who can communicate (via a shared Private Topic), and who know that every member of the group is Town. In Normal games, Masons are absolutely 100% Town...
This definition is strict, there are to be no Mafia members inside any masonry. However, I would like to point out something else on the wiki page for Mason:
[3]A Monk is a faction-flipped version of a Mason, giving absolutely confirmation that there are no Werewolves in the monastery, but potentially allowing the possibility of Mafia.
This, of course is currently not accepted as normal. For one, "Monk" and "Monastery" do not mean anything to the Normal Guidelines, and in fact would be rejected if applied to roles, as it would violate one of the guidelines for Flavor.[4] For another, the Normal Guidelines are quite clear that
However, I do have one proposition to make, which would naturally and only apply to Large Theme games:
Separate Masonries into 2 different categories, Pure Masonries and Exclusionary Masonries.
A Pure Masonry is what we currently have now, with no Mafia factions allowed inside of them what-so-ever. This is the equivalent of what we currently have now.
An Exclusionary Masonry excludes one or more factions from existing inside of the Masonry (such as how a Monastery excludes Werewolves from existing inside of them.)
Now, to properly and strictly make it clear to the player whether they are in a Pure Masonry or Exclusionary Masonry, it would be required that Exclusionary Masonries make it absolutely clear that there is a possibility that there exists a Mafia or Werewolf member inside of the Masonry, while doing the reverse for a Pure Masonry, requiring that they make it clear that no Mafia members can exist within the Masonry.
[1] Normal Game, Setup, Requirement 2
[2] Mason, excerpt from Normal Version
[3] Mason, Variations, Variation 3.
[4] Normal Game, Flavor, Requirement 2.1