Consider picking up an instrument. In most schools, if you take band, you are excused from physical education. You can pick anything from the flute to the rocking drums. It's your choice. According to her biography, Karen Carpenter took up a musical instrument to get out of taking gym, and look how far it took her with music.
Try out to be a cheerleader. Yes, you still may have to change clothes in the locker room, but you will get out of a lot of the other irksome things about gym class. You will gain popularity in doing so, but it does require a lot of commitment. You will be practicing for cheerleading a lot during the summer, and prepare to attend all the sports games. Only do it if you have a desire to be a cheerleader.
Get out of taking gym a few weeks out of the year. If dance is the sport of choice for a few weeks, get out of it by telling the teacher that it is against your beliefs. It is wrong for a teacher to make you do something that is unnecessary to your education if it is against your religion. It's never good to lie, but it also isn't right if a teacher questions you about it. Your beliefs should be respected. Request a study hall period.
Defer the gym class. In most high schools, you are only required one or two gym classes for your four years in high school. You can easily put it off for another year. In that time, you can decide if you may want to do an alternative credit, such as learn an instrument for band.
Talk to your guidance counselor. Tell her your specific reasoning for no longer wanting to take gym class. If you are sincere and ask respectfully, she can help you come up with some alternative solutions. Every school is different, and there may be some other options at your school that you never considered.