I would say that perhaps there are other options in your area. In my small town we have 1 Catholic, 1 Non-denominational, and 1 Lutheran private schools. Each has excellent test scores and they are equal in education.
I do like the Non-Denominational one since the adopted the Great Expectations philosophy and have become a charter school in the program. I like that the Lutheran school does not wear uniforms and that they offer scholarships and free lunches through the state food program.
Catholic: Same price as Lutheran
Wear dark green polo's and Khaki pants or skirts.
No scholarships or free meal programs
Not familiar with much of the religion
Lutheran: Same price as Catholic
No uniform, modest dress code, better than some schools but not strict
Free lunches and breakfasts for those who qualify
Scholarships available to those who qualify
Not familiar with their specific teachings
Non-Denominational: Nearly 1/3 higher that the other two schools
Uniforms of polo shirts and Khaki's, girls can wear skirts, jumpers, or pants
No free or reduced lunches, breakfast not offered
Religious aspect is not drilled into the kids, it is attitude and shows in the art, crafts, songs, games, etc...
So, if I were going to send the kiddo's to one or the other, and money was no factor in that decision I would choose the non-denominational one simply because of the Great Expectations aspect to their curriculum.
Here's a link, it may give you some inspiration to think about the atmosphere in the school you choose: