This statement seems rather suspect to me. From my understanding (concerning Mormon theology) faith in Jesus Christ and membership in the LDS church are only a couple of the requirements for entering the Celestial Kingdom. Your statement on the other hand bases everything on works and nullifies faith in the atonement.
Well then you don't really understand Mormonism.
Hebrews 6:10
10 For God is not unrighteous to forget your work and labour of love, which ye have shewed toward his name, in that ye have ministered to the saints, and do minister.
Several years ago an airplane landed in a river, many of the people ended up in ice cold water. A helicopter lowered a life line down to the first man who they expected to hang on as they pulled him to safety but instead he helped the woman next to him wrap the line around herself. He kept helping each person as the copter made several trips back and forth. When they finally went back to save him he had slipped below the freezing water and was gone.
For that selfless act of love that man will enter the Celestial Kingdom long before I do
But we don't all get a chance at great acts of heroism, instead we each plug along one day and one step at a time.
Salvation from sin is the free gift. We achieve this by following what Peter prescribed on the Day Of Pentecost
Acts 2
Now when they heard this, they were pricked in their heart, and said unto Peter and to the rest of the apostles, Men and brethren, what shall we do?
Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for there mission of sins, and ye shall receive the gift of the Holy Ghost.
The prick in their hearts is the Holy Ghost moving upon them, they have faith. It moves them to act upon it and repent of their past sins. They are then given the gift of baptism and their sins are washed away. They are then given the gift of the Holy Ghost by the laying on of hands. (see also Acts 8 and 19)
At this point one has entered at the gate. He is sinless but of course not perfect, the narrow path lays in front of him and he will sin again and again.
We are now going through a sanctification process, humbly partaking of the sacrament and asking the Lord's forgiveness can reset that baptismal covenant, put us back on the path. It's a life long process of recognizing our weakness and asking the Lord to help us over come them. The Holy Ghost is there to prompted us to our knees. The idea is to cultivate Christ like love, you can have all the faith in the world, you can be baptized over and over again but if you have not charity you are nothing. If you want to call that works I suppose that is but we're striping off the old man one sin at a time. God's grace comes into play by the very fact we are incapable of seeking forgiveness for every single sin, what he is looking for is the "good and faithful servant" not the perfect one.
Our Heavenly Father is not an angry God looking forward to us failing but a loving Father cheering us on, his love is always there reaching out to us. Not all of us will be worthy of the Celestial Kingdom basically because we won't all want to be there, it will be a choice we make.
Each one of our Heavenly Father's children is loved deeply and they each will be judged by the amount of light and knowledge they received during their lives on this earth. The Hindu woman will be given the opportunity to hear the gospel in the spirit world, her baptism will be done vicariously and as she accepts the atonement of Christ she will be forgiven of her sins.