Bossykate - that's interesting.
I have read the summary and skimmed the rest - there is a strong emphsis in the findings of parental involvement being a factor...and (surprising to me, I must say) that standards of leadership and governance are not significantly higher or different than from other schools. (I thought they could potentially be higher because the jobs could attract a ore competitive field and that possibly more independent governors could be more exacting!).
It does seem to me that of course many faith schools of different kinds have a v high proportion of parents who play a keen, pro-active and constructive role in their children's education, and in supporting the school, because they have taken a pro-active role in wanting their child to go there - either because they are committed to the faith aspect of the school, or are frantically 'doing their best ' for their child by pretending! The fact that children travel further to catholic scools (in this study) shows just how pro-active parents are in ensuring the right / best school. IME parents who are keen to see their children educated as well as possible are not defined by race or class...(and i am favourably / mildly surprised that there is the same diveristy in catholic schools - that has changed my percepion) but the other maintained schools will have, by default, a higher proportion of kids whose parents just don't give a damn which school they go to or how it performs, and will play little part in supporting either their child or the school.
Amongst the wider maintained sector, it is the schools with a high ration of 'involved' parents that other parents try to flock to....
Anyway, in answer to the OP - I would not pretend to have religious beliefs in order to get DS a school place, I would happily have accepted a place in the CoE school we were offered, equally I would not have pretended to live at an address I didn't (including renting for a year) but I would geuinely move to the catchment area of a school I favoured.
IMO it's about your personal standards, not about faith schools per se.