I worry such a plan will face significant legal hurdles. As suggested the building would probably not fall into the exceptions to the federal fair housing act (is that right) for choosing roommates (it's not a single family dwelling but a group of apartments in some sense).
But you EXACTLY want to choose who lives there based on political/religious beliefs (almost by definition it's impossible to be a rationalist and a dogmatic unquestioning conservative christian). Also by aspects of family makeup in that you don't want people living in this community to import a large extended family to live with them if that family doesn't share the values/concerns of the other people living in the community.
Basically, I think the degree of control you want over who lives in the building may be incompatible with various non-discrimination laws. However, one could probably find 20 families that could jointly purchase the building as condos to avoid this problem.
But I don't see any way around these problems in the long run. As the original group breaks up it will be hard to replace them without legally problematic screening.
If the descrimitation laws consider rationality political a way around might be to declare the whole community a religious community. Monastries have no problem picking their members via religion.
Rationalists like to live in group houses. We are also as a subculture moving more and more into a child-having phase of our lives. These things don't cooperate super well - I live in a four bedroom house because we like having roommates and guests, but if we have three kids and don't make them share we will in a few years have no spare rooms at all. This is frustrating in part because amenable roommates are incredibly useful as alloparents if you value things like "going to the bathroom unaccompanied" and "eating food without being screamed at", neither of which are reasonable "get a friend to drive for ten minutes to spell me" situations. Meanwhile there are also people we like living around who don't want to cohabit with a small child, which is completely reasonable, small children are not for everyone.
For this and other complaints ("househunting sucks", "I can't drive and need private space but want friends accessible", whatever) the ideal solution seems to be somewhere along the spectrum between "a street with a lot of rationalists living on it" (no rationalist-friendly entity controls all those houses and it's easy for minor fluctuations to wreck the intentional community thing) and "a dorm" (sorta hard to get access to those once you're out of college, usually not enough kitchens or space for adult life). There's a name for a thing halfway between those, at least in German - "baugruppe" - buuuuut this would require community or sympathetic-individual control of a space and the money to convert it if it's not already baugruppe-shaped.
Maybe if I complain about this in public a millionaire will step forward or we'll be able to come up with a coherent enough vision to crowdfund it or something. I think there is easily enough demand for a couple of ten-to-twenty-adult baugruppen (one in the east bay and one in the south bay) or even more/larger, if the structures materialized. Here are some bulleted lists.
Desiderata:
Obstacles:
Please share this wherever rationalists may be looking; it's definitely the sort of thing better done with more eyes on it.