Catholic colleges typically accept transfers from any college, regardless of religious affiliation. The considerations made by a Catholic college toward accepting a transfer student almost never include the religious standing of the college they are transferring out of. Instead, transfer students are weighed by the Catholic college's admission's requirements.
The admission requirements will vary by college, so students need to be sure to carefully read over the admission requirements of the Catholic college(s) they plan to apply to. These requirements are in place to assess the applicant's academic performance, completed coursework, and personality to determine how well they align with the Catholic college's standards and values. Like applying to college as a freshman, there are going to be essays, transcripts, and recommendations required as part of the transfer application process. Students need to be sure to turn in all required documents and complete all parts of the application before the deadline, which may be different for transfers than first-time college students.
As with other universities, Catholic colleges use the credit hour system to measure a student's degree progress. It is important to note that not all colleges accept the same classes for the same number of credits. This means that while a student may have 75 credit hours from the college they are transferring from, the Catholic college they are transferring to may only accept 68 of them. This has to do with the Catholic college's academic standards, accreditation of the course/university it was taught at, or differences in course content. There are ways to appeal/petition for classes to be accepted that are not initially, but it is still at the discretion of the Catholic college as to whether they will accept or not.
Students should be sure to discuss transfer credit policies with the admission's department of the Catholic college they are planning to transfer to for more detailed information about what will be accepted and how to petition if needed.