I am far from an unbiased source, since I was raised in one of those 80%+ Mormon small towns out West (and am still working through the residual effects), but PBS's Frontline recently did a
two night series that manages to give a fairly balanced view of the church, its teachings and its history. (The link gets you to the internet versions for your viewing pleasure.)
In the second night, when they tackled some of the tougher issues, they boiled it all down to this: Mormonism is extremely dedicated to the idea of the nuclear family. If you fall easily within that traditional model they can be tremendously empowering and supportive.
If you fall outside it, as do not just gay men but also much more morally neutral (from their point of view) creatures as women who don't want to get married or even are married and just don't want to have children, it can be very, very hard on you simply because you fall outside the values of the community.
It is often hard to correlate any church's practices to its beliefs, since (for example) being family friendly can mean everything from welcoming small children to the service to condemning the use of birth control. Mormons
do condemn gays as persons having non-procreative sex outside of marriage. Interestingly, however, they equally frown upon anyone who is in that position. In this way I find them less hypocritical than most fundamentalist religions whose policies would seem to say the same thing, but who have little problem with hetero fucking around, divorce, and abandonment of wives and children but feel the need to preach against homosexuality virtually every Sunday. Mormon families
can be close, and therefore supportive, of their gay children albeit in a rather condescending way of offering love to a sinner.
Sorry if this rambled a bit, but one final thought for the OP. My best guess is that the young man you are playing basketball with already strongly suspects you are gay. Young men tortured over their sexuality make particularly good conversion targets. (Not saying you are tortured, but if he thinks there is a chance you are his training is to go after you.)