The advice is always to put your catchment school as one of your choices, even if it's the last choice. Otherwise, if you don't get into any of your choices and your catchment school was oversubscribed, you'll be allocated a place at the school nobody else wanted, probably miles away.
You might be surprised at how Christian the "non-faith" schools are. We had a "choice" between (ie realistic chance of getting into) 4 schools for DS, 2 C of E controlled and two community primary schools. In the end we felt that the religious element was less of a distinguishing feature than we had expected it to be - which was a shock, but meant we ended up with the C of E schools as our first and second preferences as they were by the far the better fit for DS in all other ways (facilities, behaviour policy, approach to teaching, size etc).
All schools are mandated not only to teach RE but also to have a daily act of a worship of a "predominantly Christian nature". RE in the community schools in our area is taught to a syllabus set by the LEA, whereas the C of E schools use a syllabus set by the local diocese, but both cover multiple faiths while being quite strongly weighted towards Christianity. The community schools locally make much of their links with the C of E parish church etc and one of the two we viewed seemed almost more overtly "Christian" in flavour than the two actual C of E schools we visited.
I think generally speaking, if the C of E school is the only school in the area (eg "the village school") then they are more likely to look and feel similar to the local non-C of E community schools, because they are schools for the whole community and their intake reflects the catchment.
We have found DS's school so far to be sensitive to the fact that some of its pupils come from families of different faiths than Christianity. It's part of their stated policy to foster respect for different religions and world views, and, for example, to ensure that children from families of other faiths are able and encouraged to mark their major festivals within school. You can withdraw your child from collective worship if you choose to (FWIW we haven't - DH follows a different religion and I am an atheist, but there are many times in life when you have to attend religious occasions of other faiths, so learning to be respectful of others' beliefs might as well start early!) I guess the C of E school is more testing for me as an atheist, the school's culture is rather less accepting of a position of "no faith"! but other faiths are definitely respected and supported within school, both in policy and in practice.
Speaking as someone who didn't want a "religious" school for my son, I'd say look at all the options with an open mind and weigh it in the balance together with the other factors that go to selecting the school that's the best fit for your child.