Class of 2019 wrote:
To everyone asking if I am Mormon: I’m not, but I was raised in a very conservative evangelical faith and the honor code would be a non-issue, even a plus. I think it would be just fine
If it doesn't faze you now, it won't faze you when you're there. Referring to culture, there are some odd Mormon culture-isms that will take getting used to, but you'll generally be welcomed. You'll also find that runners are sort of the same oddballs everywhere you go, Mormon or not.
To your original question: You would be a desirable recruit, no doubt about it. Tuition at BYU for non-Mormons is ~$11k/yr right now. Living expenses are cheap in Provo. You'll have to figure out how much money it would take to make that an attractive option. BYU doesn't have a ton of money to spread around.
IMHO, Ed Eyestone is one of the top-3 coaches in the NCAA. That should weigh into your consideration.
Academically, BYU has some strong programs. Also should be considered.
The hardest social aspect for you might be dating. Maybe 90% of BYU girls won't date someone who isn't Mormon. Consider that if it's important to you.
Reach out to the coaches and schedule a visit. They also hold a summer XC camp that would be a great chance to check them out.