Yes, admission to vet school is extremely competitive, even more than medical school. (There are not as many veterinary schools so space is very limited.) And sadly, the veterinary profession has a high rate of suicide. So with a demanding and stressful course of study and profession in the future, the last thing in the world your son needs is the stress of an anti-science church or curriculum!
Your son should at some point start volunteering at shelters, wildlife rehab facilities, community spay/neuter clinics and the like if at all possible. He should learn all he can about cats, dogs, large animals, exotics (small furry pets, birds, snakes, etc.). He should visit zoos and aquaria. I’m sure he will have a great time in his chosen path, as he sounds really smart.
There are really good free or cheap science courses on http://www.coursera.org and www.edx.org. (Consider working through a course together since he is still young.)
Best of all is http://www.hhmi.org/biointeractive with hundreds of free science resources.
Best of luck!
btw, Consider following the veterinarian Dr. Marty Becker on Facebook–I’m pretty sure he’s a Christian.