I haven’t sat on a Med school admissions committee, but I was involved in a residency committee for years. We accepted 12 residents per year (big program) and usually had several LDS applicants. It would be challenging to look at 30-40 solid applicants from the same school when you only have 100-120 slots and decide how many of them you want to take when the applications look very similar.

While I think you have a point that they are looking for people that are different. I do think there is a religious bias based on my brother's experience. When applying for a residency, he got 98th percentile in boards, was a college athlete and had other things to set him apart from others.

In his first interview, the interviewer said "You aren't one of those mormons are you?", it was a little awkward when he said he was.

With the match system it's hard to say if he would have gotten chosen, but it went from being a top choice of his to being ranked towards the bottom. Ultimately, he got into his top choice, but he was disappointed with the interview experience.