5 or 6 people made their opposition clear in General Conference.
Many faithful Mormons have reacted with varying degrees of anger or disdain towards that handful of objectors. I can understand having that kind of reaction when somebody disrespects somebody you care about but to be honest, I'm glad they did it. I do not say that out of any sympathy for their causes. I'm also not convinced that it was necessary for them to be so disruptive in how they expressed themselves.
I see three possible situations here:
1. They have a legitimate reason to object.
To me this the most far fetched thing possible, but the whole point of calling for a sustaining vote is so that if there is a legitimate reason why a certain person should not hold a certain office, it can come to light.
2. They are sincere, good-hearted people who think they have a legitimate reason to object when they do not.
If this is the case, objecting will lead to them receiving the counsel and information they need to realize their mistake. Back in 1980 when there were objectors over the issue of the church's opposition to the Equal Rights Amendment the objection was only leveled at the first presidency, not the Quorum of the 12, so the objectors were invited to meet with the President of the Quorum of the Twelve (President Hinckley) to address their concerns. In this case, since they objected to both the First Presidency and the Quorum of the Twelve they are invited to meet with their Stake President. Hopefully this will lead to them obtaining a better understanding, realizing their mistake, and gaining a renewed testimony.
3. They have gone apostate already.
It is tempting to assume that this is the case right off the bat, but in our hearts we should be open to the possibility that they are honestly mislead people. If however they truly have gone apostate then it is still a good thing that they have spoken up. It is in their best interest to be released from covenants they do not intend to keep, and it is in the best interest of the church to keep an apostate from appearing to be a faithful member.
There is a difference between being able to do something, and whether you should do that thing or not. In objecting to sustaining a leader, it should only be done in the first case, but no matter what case it is, the person doing it is likely to see their objection as legitimate. The good thing is that in any of the cases above, their objecting begins a process that will lead to a
better situation for the church and the individual as long as truth is not resisted.
Can vs. Should
The difference between 'can' and 'should' applies in another recent event in the church.
Recently, Elder D. Todd Christofferson remarked that members are free to hold as a personal belief views on same sex marriage that are not in line with the church's position. This makes sense as the requirements for baptism (ie: membership) in the church don't require a person to know and accept 100% of the church's position on everything.
If a person believes in God, has faith in Christ, believes the restoration, commits to live the gospel standards, and doesn't have any past sins of a serous nature there is nothing to stop them from becoming Mormons. Every convert, and every member born in the church, is carrying around some idea or belief that is not correct. The purpose of the church is to create an environment where we learn and grow. As we attend church, study the scriptures and live the gospel, God can work on us to help us shed false ideas and replace them with truth.
It would be a mistake however to assume that because a member can hold such a view, that they should. Nothing in what Elder Christofferson gave any endorsement to a pro same sex marriage position, in fact he made it clear that acting on such views by organizing against the church, or trying to pull people away from the church are not acceptable, and that the position of the church with respect to opposing same sex marriage is not going to change. There is no apology from the church for it's efforts to keep same sex marriage from being legalized, and no acceptance of gay marriages as moral or legitimate in the eyes of God.
I recognize that there are solid members with testimonies of the gospel who feel tension between the position the church has taken against same sex marriage, and their personal feelings on the issue. Often this strikes very close to home where there are desires for a child or other family member or close friend who is gay to be happy and have companionship. A life of faithful celibacy seems like a hard thing to ask of somebody, yet that is what God asks.
Over the short term, that tension can be maintained and lived with, but I hope that those members are seeking for a more harmonious relationship with the gospel during that time. God loves all people, and he wants the best for each person as well. His commandments are not given without an understanding of the complexities of mortal life and our own emotions.
Since God can truly love a gay person and also hold to what His moral laws decree at the same time, then we can also truly love those around us no matter what their orientation, without compromising on what is right in God's eyes. We can cling to a view on same sex marriage that is contrary to what the church teaches, but we should seek to harmonize our hearts with the gospel.
We just have to learn to love as God loves. I fear that those who give up on seeking after that may be expressing objections of their own in some future General Conference. They can do that, but that doesn't mean they should, and it doesn't mean eternal consequences can't result from it.