Single-sex colleges are almost a thing of the past. There are less than 75 remaining in the entire United States. Although 75, less than 10 are all male campuses. It seems that females are the main ones more comfortable with the idea of a single-sex college. Most men seem to like the idea of having women around while being college.
All single-sex colleges are private. The two public colleges that males were only allowed at are the Virginia Military Institute and The Citadel in South Carolina. This changed recently however, when they both lost legal battles and had to admit women. Since both of these schools are funded with public money, the courts ruled that they must be equally spent, no matter what the gender of sex. Since the remaining single-sex colleges are private, there are no laws governing what they can and cannot do.
The most common colleges that only allow females to attend are Bryn Mawr, Smith, Mount Holyoke, and Mills. Radcliffe and Barnard are all female, but are components of Harvard and Columbia universities. Harvard and Columbia service bearing universities to the two, which allows them to be independently owned and operated. If you are a student applying, you would be admitted to Bardnard, not Columbia and vice versa for Harvard.
It is estimated that around half of four-year private colleges are associated with a religious denomination. Most of these colleges are either tied to a Christian or a Catholic denomination. There are also some Baptist and Mormon colleges as well. A few examples of these colleges would be: Notre Dame, which is Catholic, Baylor, which is Baptist, and Bringham Young, which is Mormon.
Most colleges will accept any student applying, regardless of their faith. The way the colleges see it is that money is money, no matter who it comes from. Notre Dame uses priests as professors, which is one common practice that religious denomination schools will use.