Wants to go to the Y to be a problem, make a statement, be a thorn in the side of the church as a revolutionary. If they Vehemently disagreed with something as polarizing as the churches stance on homosexuality they would vehemently dislike BYU and the the people that agreed with such a stance.
I would very much hope they would not be allowed.
That said it depends on the bishop or church providing the EE.