The question is why -- what's their motive? I'll say from having spent some time with members of the group in various adult forums and similar activities, none is especially knowledgeable on matters of religion. These, after all, are the folks who brought us "Angelicanism" (and have "temporally" locked out the community groups).
Did they seize the parish because eight or a dozen were adamantly opposed to becoming Catholic? A few did have obstacles, but others, like Mrs Bush, did not. Indeed, Mrs Bush is a respectable lady, Catholic or otherwise. Andy Bartus, who worked hand in glove with Mrs Bush and others, became a Catholic priest himself, though not, apparently, in the position he preferred, which would have been pastor of the then-wealthy St Mary's parish.
So what did they have in mind? The best theory I've heard from several sources, including the vestry and the thinking on the Freedom for St Mary's site, is that the squatters wanted to sell the property. This is certainly a persuasive explanation for the sudden appearance of Crosby Doe on the squatter central committee (misleadingly called its ":vestry" on earlier versions of its web site). Doe, who had not been involved in the parish prior to the seizure, is a realtor who specializes in historic properties.
But what we've seen since 2012 is that the squatters apparently have had no intention of running a viable parish, and indeed currently seem to be in the process of shutting the place down.
I assume we will learn more as events proceed. In the meantime, the squatters finally rescheduled Christmas Eve for December 24.