I don't think there are any schools which absolutely require students to belong to the religion with which they are affiliated, but they may require students to abide by the rules of the religion and to attend services or take religion classes. I'm not familiar with the College of St. Rose, but I've worked for 20 years at Catholic universities (and I'm not Catholic), and I know that there is a huge range of devoutness among Catholic universities, ranging from some which are extremely strict to others at which it is almost possible to forget that they are Catholic.