I have heard various people of other denominations and religions say they have a problem with the belief that Jesus is the “only way” to achieve happiness in this life and exaltation in the life to come. I believe this is due to a fundamental misunderstanding of what the verses that teach this mean.
I always have interpreted that teaching to mean that the GOSPEL of Jesus Christ is the only way - which I take to mean the principles He taught and the end result of those principles, spelled out in the Sermon on the Mount and encapsulated in Matthew 5:48, Romans 8:17 and other passages in the Bible. That's the only interpretation that makes sense to me in light of perhaps the most fundamental reason for the Restoration - the need to re-establish the universal power of the Atonement of Jesus Christ that Paul taught so clearly in 1 Corinthians 15 - especially verses 21-22.
I believe that is why we can say that those of other religions who live according to those principles can be saved and exalted just as Christians in this life can be - that they lived according to the principles of the Gospel and the light of Christ they brought with them to this earth, even though they "knew not Christ in this life".