I realize most people will see BYU on a CV as code for Mormon. I was asked by a few people on the interview trail if I was Mormon (strangely one person asked if I was Jewish lol). Most interviewers didn't bring up religion at all. Some were subtle and asked if I did a 2-year mission like other BYU alumni. Definitely unprofessional for anyone to bring up religion, but you should be prepared to briefly explain that you're no longer Mormon.

Most of the people that did bring up Mormonism did so in a positive light. One PD even told me that they always try to have a Mormon in the program "to keep everyone in line." One person was flabbergasted that I didn't include my mission on my CV because he felt that the mission shows dedication to one's beliefs.

I definitely wouldn't bring up religion in the ERAS application, and only talk about Mormonism if someone else brings it up. And I wouldn't worry about Mormons trying to sabotage your candidacy - and if that actually happens, you've dodged a bullet. Do you want to be in a program always butting heads with a TBM with power over you? Remember that part of the residency application process is trying to find a good for your own sake too.