Female doctor- no handshake, but ok with medical touch during examination

I (obviously male body, though I actually identify as genderqueer) recently visited my doctor for the first time. She declined to shake hands during intros "for religious reasons", and even dodged around my instinctively outstretched hand so as not to accidentally touch it. During the examination itself though, she repeatedly touched the bare skin all over my body during the skin cancer screening, while examining various moles and such. She's educated at one of the best medical schools in the world, and is a highly effective doctor. I would like to be polite to her by understanding her preferences a bit better, and not putting her in a position where she needs to tell a patient "no, for religious reasons". I'm not asking for whether her behavior is "correct" or not. I'm merely trying to understand the likely motivations behind her behavior, and how I might be able to avoid putting her in a potentially uncomfortable position in the future. If it matters, I live in California.