There is a short answer to this question, and it is "Yes."
The long answer deserves a little more explanation.
Let us suppose three cases, all true stories and the details of which I am personally acquainted:
1) A man marries in the temple, he holds several significant callings throughout his life, including bishop, stake president and stake patriarch. At his funeral, some of the grandchildren begin sharing their experiences with each other they had with their grandfather. They discover that several of the grandchildren were sexually abused by this seemingly faithful man. At the time of his death he was serving as the stake patriarch, routinely giving inspired blessings to the young members of his stake, many of whom were the same ages of his grandchildren when he was secretly abusing them. The secrets of this family went undetected and undiscussed for almost two generations. From all appearances this family was a "model" LDS family to all who knew them.
2) A Relief Society President came to confess a secret sin to her bishop. She had become infatuated with a co-worker. They traded e-mails, innocent enough to begin with, but soon the innocent exchanges turned into increasingly explicit love poetry. Soon they were meeting for movie outings during the day. Then lunch followed the movies, then the movies became more and more explicit. Their love for each other blossomed. She was getting attention from this new suitor she was unable to find at home with her husband. A disciplinary council was convened on her behalf. She wanted to remain with her family and her husband. She was disfellowshipped, but a year later was reinstated.
3) A revered Church leader who had served as a bishop, a stake president, then later as a mission president confessed many years into adulthood he had been romantically involved with his administrative assistant for years. He was excommunicated. His missionaries were devastated, the members of his former stake were disillusioned, and many questioned the inspiration involved with the leaders who had called him to all these positions. In time he wrote a book about his life. His repentance was deep and real and painful. But still others questioned his judgment in profiting from his sins of the past. The secrets he harbored about his behavior, notwithstanding, his wife and family rallied around him and he was later re-baptized and all his priesthood blessings were restored in time.
Worthiness, then, becomes a matter of degrees. We get on a path at baptism leading toward exaltation and eternal life. Our path twists and turns through mortality. Few walk a "straight and narrow" path flawlessly. I know of none who has or ever will. When secret sins are harbored and remain hidden sometimes for years, and yet men continue in their priesthood duties undeterred through many temple recommend interviews, lying and covering up their past sins without remorse until they are "caught," of course there are logical questions of worthiness that arise.
There is a corollary here too: Parenting. Sometimes children get the vibe from their parents who are driven by the need to have perfectly behaved children that they never will be "good enough" to measure up to their parents' lofty expectations. They become discouraged and give up. The quest for perfection is simply too much for them to continue. I labeled this "The Impossible Gospel" many years ago. Some sons think they can never be "worthy enough" in their fathers' eyes, and some daughters think they will never be "competent enough" in their mothers' eyes.
Of course, these thoughts are silly and should not stand in our way to accomplishing what we know we must as we mature and separate out from our parents' watchful care taking of us. The transition from being parented to becoming the parent is often traumatizing to some because of these perilous and false thoughts and expectations. I hope no one gets trapped in this stage of natural and normal progress in mortality.
Here's the reality of parenting - no matter how "great" our parents were, we are all scarred by what parents do or don't do to us and for us. Be kind with each other. Forgive generously. Move on gracefully without harboring the painful memories and replaying them again and again. Don't get stuck in misery.
Patience with each other is required. Harsh judgment for those who falter is not the same treatment we would choose for ourselves. And so we must become as patient as Heavenly Father must be with us. We learn by doing.
Have you ever had the experience of hearing about someone who was called to a responsible position in the Church, and yet based upon your own personal interactions with that person in their past life you know them to be "less than" worthy enough to perform in the office to which they are called? Do you wonder if they might also be having feelings of being "less than" they wish they were? Do you believe these are almost universal feelings others may have? Do you assume they never accessed the benefits of Christ's atonement in their life the way you have have in yours? Are you willing to condemn them for past sins you KNOW about, and yet exonerate yourself for your own hidden sins? Do you take comfort in the public display of another's weakness and remain smug that your secret sins go undetected?
We are all sinners. We all come short of the mark when it comes to the lofty ideals of the gospel compared to our actual performance in mortality. Remember, this is all a test, and most are struggling just like you when you flounder with the details. When long-cherished sins are finally exposed to the bright sunlight of truth, we are grieved, and those who are closest to us are likewise affected and grieved. Yet none of this invalidates what a fallen, imperfect person has accomplished for good during their lives. While we must develop understanding and empathy for one another, it may be just as important for us to give ourselves some of the same too.
The requirement is repentance, NOT perfection or the expectation of it any time soon.
Some wives punish their husbands brutally for their mistakes, and some find it difficult to excuse even when sincere repentance is in evidence. A breach of trust is difficult to repair. That's when Satan is at his most powerful in our lives. He thrives on harsh judgments. He is a master at hardening hearts. "I trusted you then," one would say, "and you betrayed me. How can I ever believe anything you ever say again?" When she begins to examine her own life, however, she finds she has withheld as much, then she is fearful she will be treated with the same judgment from her husband she has imposed upon him. And Satan drives those wedges of doubt and fear deeper until the marriage splits. He loves the conflict, the drama and the anguish growing out of the sins he promises will have no consequences. His greatest lie is the one about "victimless sins." Believe me, there is no such thing. Actions bring consequences. When we pick up a stick, we pick up both ends.
What is needed in all these cases is a broad brush of forgiveness. I've learned this is very hard work. When one of the combatants steps away from the conflict, there is no longer a war. When I have been discouraged with relationships, especially family relationships, I have heard a gentle whispered encouragement from my Mother, who died fourteen years ago, "Try one more time, David." It is an unmistakable voice of patience and love.
Of course, there are many situations where forgiveness and repentance just aren't enough, but those situations often suffer from a lack of willingness to extend the balm of Gilead to each rather than a lack of power to heal from the Savior. His love is perfection.
I counseled a couple for many months who found it difficult to remember why they had gotten married in the first place. I granted a temple recommend to the husband with reservations that I knew he was "not worthy" to go, but hoping to rekindle his love for his wife. I instructed my stake president about the course I was recommending to them and asked him to sign this brother's recommend despite my misgivings. I was acting on a prompting that suggested if they could go through an endowment session together, then spend an hour sitting side by side holding hands in the Celestial Room, then going on a sealing session together, there might be a chance to rekindle their marriage covenant. The last time I checked (and this was many years ago) they had six children.
I suggest we trust God. All our husbands and wives are His children first. He knows them better than we do. He also understands the fallen condition we face in mortality. If He had to rely upon conferring priesthood responsibilities only on "worthy" people, He might have easily decided to give the priesthood to women. That way He might be better assured of all the ordinances being performed in perfection.
However, mortality is what it is. We are sent here on a mission to purify ourselves through the blood of Christ. We are also told there is no other way, and no other name given under heaven by which we can be saved from sin and death and made pure. We are told we must never play in the gutter and avoid soiling our best Sunday-go-to-meeting clothes. But in mortality we routinely find ourselves in the gutter. . .
And it's hard to avoid getting dirty.