Unless you can self-fund attendance to the school (i.e. get a full ride merit scholarship without needing any money or financial aid form cooperation from your parents), then applying to a school which your parents won’t pay for is a complete waste of time and money.
Regarding the specific religious affiliation, is it that they object to University of Puget Sound’s rather loose ties to the United Methodist Church (based on the list of colleges at http://talk.collegeconfidential.com/college-search-selection/1700245-differences-between-pacific-northwest-lacs.html )?