Columbia University released this study very recently looking at the congruency of public opinion and policy related to homosexuality:
The study made some interesting conclusions, most notably that there is no pro-gay policy bias, to the contrary, where policy is incongruent with public opinion on that policy, it is in favor of the conservative minority. This chart is also very illustrative, in my opinion, of the big mistakes the leadership of the church are making if, as many suppose, they are largely in favor of changing church policy concerning treatment of homosexuals.
Note that while public opinion in the US has generally moved progressively, the movement in conservative states has been dramatically slow relative to the more liberal states. Utah, Oklahoma, Alabama have moved positively over the last 15 years by only about 5%, whereas New York, Vermont, Massachusetts, have moved upwards of 25%. This is statistically amazing.
At first blush, one might think that this is the result of "gay-flight" from conservative states to more accepting states. Alternatively, the prevailing theory that if one knows and associates with gays and lesbians, their attitudes will change, may be the cause - that more liberal states will have larger number of "out" and "open" homosexuals and as a result, attitudes become more positive But demographics do not bear either of these theories out.
This survey from 2007 actually indicates the opposite.
Demographic migration among same sex couples has generally followed those of the population at large - to the south and west - ie. to conservative states. Moreover, socially conservative states showed above-average increases in homosexuals coming out over these past 15 years. For example, Utah went from 33rd to 14th in ranking of concentration of same-sex couples from 1990 - 2006.
So notwithstanding the fact that same-sex couples are becoming more prominent in conservative leaning states, the progression of public opinion with respect to homosexuals in those same states lags far behind that in more liberal states.
The Columbia study theorizes that public opinion moves fastest when particular issues are particularly salient. That is to say - the more the issues are talked about and discussed, the faster people are to accept a more progressive view point. In states where the public was more liberal 15 years ago, issues such as gay marriage, civil unions, adoption rights, visitation rights, etc. have been front and center in policy debates and correspondingly, states where these issues don't come up in legislative discussion or primary elections, progression has been very slow.
The study discusses this in more detail, but there are several reasons why salience leads to progressive public opinion and, eventually, congruence with policy. It's also interesting to look at factors which influence a in-congruity - ie. policies which are favored by majorities or supermajorities, are nonetheless ignored by policy makers. These are largely due to very vocal, very well funded interest groups.
If, as so many suppose, the Church leadership is in favor of changing policy on homosexuality, while simultaneously limiting the unavoidable schism which will accompany it, they should (a) present issues rather than general theological ideology (ie. discuss gay marriage and gay ordination rather than the theological morality of homosexuality in general) and (b) they should actively and affirmatively promote church-wide discussions of these issues.
Contrary to what I'm sure they would assert, over the last ten years, the church strategy has been the opposite. Discussion has been minimal at best and discouraged at worst. Resolutions brought at World Conference have been squashed, no materials prepared for discussion, no articles in official publications or online. In addition, discussion that has occurred, most notably through the work of the now-defunct Committee on Homosexuality and the Church focused very broadly on the "homosexuality issue" in general and not on specific policies.
Given this, it is likely attitude toward homosexuality within the Church has and will continue to follow the slow path of Utah (and Missouri) rather than the pace of more progressively lead states. But the Church has an even bigger problem. While demographic trends in the US apparently aren't heavily affected by politics or policy (although look at this latest study indicating that migration to conservative states may be slowing: http://www.esquire.com/features/data/red-states-blue-states-0709) churches are most definitely not immune to loss and, more importantly, lack of gain, due to disaffection with policy and leadership.
Just look at what the Church continues to say about contributors to the World Church: http://www.cofchrist.org/news/2009/june/wcfb.asp
"The strength in World Mission Tithes is coming from people over fifty. The heroes of this story are the seventy-, eighty-, and ninety-year old people who are carrying the load."
One can make any amount of assumptions based on this trend which has followed closely the demise of the population/budget of the Church, but all studies show that support for homosexual rights declines with age - especially in religious settings (http://pewforum.org/docs/?DocID=38).
It would not be a leap therefore, to assume that the Church, by vehemently adhering to conservative social policies on homosexuality, are discouraging growth and encouraging loss among those who would be more likely to support policy change. Moreover, as within those who continue to support the Church, the strategy of ignore and delay with respect to these policies, is more likely to cause the progress of membership opinion to stagnate.
Bottom line is - over time, the Church will become more and more composed of conservative thinkers whose attitudes toward homosexuals will progress slower and slower relative to the outside world. This does not support the continual pleas from the First Presidency and the Leadership in general, that progressives should be patient, should be quiet, and should be deferential to current policy, in order to bring about positive change. Quite the opposite.