I can appreciate how it would be extremely difficult for (say) a non-religious person choosing (say) between a good faith school and a crap non-faith primary, or someone who were ideologically opposed to private education choosing between a good private school and a crap state school.
Personally I would always try to give my principles first chance, but I would probably be prepared to change my mind if I could see that my child was really suffering as a result.
However you seem to be in a better position than that - the "fourth best" school, whilst not being religious, private or pretentious, is not dire either! So why not give the school a chance?
I'm lucky enough to live in an area where there is an outstanding Catholic primary (we are atheists) but also a "second best" primary which is not appallingly crap. So that's where my DS will be going. However, if we weren't lucky enough to have such a good second best I might well have compromised my principles. I'm glad I haven't had to do so and I wouldn't judge anyone for doing the same.
It's not ideal and it's not something I would ever attempt to dress up as anything other than compromising principles, but I can see why people do it. You put your children first in every area of your life. That's what parenting is about. I'd save my judgey pants for people who pretend that's not what they're doing, rent houses in the catchment, forge applications, or try an justify their compromise by saying it's only because their children are so particularly special / advanced / gifted (as though that somehow means they deserve a superior education compared to other kids).
I have done very well in life despite having the shit kicked out of me in a comprehensive school, although there are still a few bastards from those days I'd happily run over if the chance presented itself, I wouldn't go back and change schools. My parents offered to do so (would have meant a BIG compromise for them) but I quite rightly decided that kids at the local private school were probably just as likely to be vicious little bastards and I would still be the "weird kid". Ultimately I think that as a parent you can make a difference to your kid's education whatever school they go to, and you can also, hopefully, make a difference to the school itself.