We used St Mary's school and nursery and were very happy with them. The staff are very kind and friendly. They know all the children (not just the ones in their own class) and treat them as individuals.
There is nice collaboration across the year groups for things like Christmas nativity and house/responsibility time/pupil council/school captains and the after school activities are probably more inclusive than at the bigger schools. For example, you can go to the badminton or table tennis club even if you're not super sporty and nearly all the older pupils joined the Glee choir (boys and girls) whereas the Newton Glee choir tends to be just theatrical/dancing mad types.
Yes, St Mary's are an Episcopal school attached to the Episcopal church but they are not giving extra religious instruction and there are no daily prayers or anything like that. They have a weekly assembly which the rector/vicar/minister is involved in but it is basic Christian and moral input of a type you would get at any primary school end of term service. The term 'faith school' seems to make people think it's super religious but there's no mystery about it and, as they make clear on their website, there is no requirement to have any family connection to the church.
Parents remove children from all schools, including Newton and Dunblane, for all sorts of different reasons. If your child likes the buzz of a large class (30+ in many years) and a large potential friendship pool, they might be happier at Newton or Dunblane. It's also useful to suss out who's who before going to high school which can be a pretty tough environment, even in Dunblane.
At St Mary's some of the year groups are very small which is fine in the lower primary years and the children play together with others in their composite class. It is potentially a bit more difficult further up the school though if you're in a group of, say, five boys and one girl, particularly looking ahead to high school transition time.
The issue of St Mary's children struggling to settle at Dunblane High appears on here from time to time but, again, there are children from other schools struggling to settle at Dunblane High as well. I would agree there is quite a strong Newton Primary/Dunblane Primary divide at the high school but, as with life, personality type is probably the key factor in determining how well anyone from outside the Newton and Dunblane goups (i.e. St Mary's young people and those on placing requests) will fit in. If your child is quiet, they will probably find St Mary's more manageable. If they're extrovert, they'll probably do fine at high school whatever primary they've come from.
If you like St Mary's, just go for it and don't worry about what people on Mumsnet say!