Not really.
The LDS Church took a beating, from the inside and outside, for aggressively supporting Proposition 8 in CA during 2008. Since then, the Church has moved on to other battles in the cultural wars rather than to continue to take on the homosexual-rights activists for several reasons.
1. Church leadership felt like it was left holding the financial bag after other evangelical denominations failed to come through with promised aid in the fight against Proposition 8. Top church officials were heavily involved in the creation of the National Organization for Marriage (NOM), the primary player over the last decade in the fight to outlaw gay unions.
2. Church leadership feared that continued support of anti-homosexualsexual marriage measures would continue to generate negative publicity which in turn would limit the ability of its farflung missionaries to engage potential converts.
3. The Church wanted to be more welcoming to its members who are afflicted with same-sex attraction.
4. Mitt Romney, perhaps the highest profile Mormon in the U.S. today, had advocated membership for all homosexuals in the BSA since 1994. The chuch did not want to harm Mitt Romney's 2012 presidential campaign.
5. Another high-profile Morman, Jon Huntsman Jr., former governor (R-UT) and former ambassador to Red China under POTUS #44 BHO, announced his support of homosexual marriage in FEB 2013. He also signed on the amicus brief that opposed the DoMA which is currently before the SCOTUS.
6. BSA National President Wayne Perry is a lifelong Mormon. He convinced the Mormon leadership to change its adversarial position against homosexuality in Scouting, which went back to the 2000 SCOTUS case, BSA v Dale.
You wonder whether BSA president Wayne Perry may have a close relative who is homo. I think many prominent people who have sided with the homos have close relatives who are homo—look at Portman who came out to reveal his support for gay marriage because his son was gay. There must be top people in government, corporations and even religious institutions who have close relatives who are homosexual. The homos are taught to play on the sympathies of their families and relatives to get their way.