You could try flagship state universities in religiously conservative states. It doesn’t sound like Brigham Young U, Oral Roberts U, or Liberty U appeal to you, but maybe secular alternatives like U of Utah, U of Oklahoma, or U of Virginia would fit.
Your options would obviously improve if you considered religious schools. Some may require students to profess a specific faith, but others may not. You don’t have to be Mormon, for example, to attend BYU.