A few years ago, Joseph Fielding McConkie had these thoughts on the Church’s moves towards “ecumenism”, or trying to get along with other religions:
The Ecumenical Movement
As a young man I was commissioned as an officer in the Army of the United States and assigned to serve as a chaplain. My first duty was to report to an officer’s training school at Fort Hamilton in New York. There the Chief of Chaplains, a three star general by the name of Charley Brown, told us that our commission was to be the grassroots of the ecumenical movement. There were one hundred of us in that class, representing every major faith in our country. We were instructed to work together. We were informed that it was a violation of military law for us to proselyte for our own faith. Were I to attempt to teach Mormonism to someone who was not already a Latter-day Saint would have been grounds for a court marshal. Such is the cost of an ecumenical movement.
I appreciate the observation of Elder Maxwell, who said, There is today more ecumenicism, but there is also more shared doubt. More and more people believe less and less but they do believe it together. The fewer the issues, the easier it is to get agreements. The fewer standards there are, the less there is for congregations to rebel against. Since knowing is tied to doing, and doing to knowing, there is an awful cycle in all of this.
By revelation, we as a people have been charged to stand independent of the world (see D&C 78:14). In a directive to priesthood leaders President Packer stated, It is important to maintain a cordial and cooperative relationship with the leaders and members of other denominations. Representatives of the Church should not join interfaith organizations that have as their focus ecumenical activities or joint worship services. Interfaith relationships should center on moral values and on community betterment. 
In short, the danger of trying to be liked by other religions is that they might think we are trying to be like them. Which should never be the case. I wonder which is more dangerous: being the weird, unliked, persecuted “cult”, or the big, popular, respected religion? Which fosters a faster deterioration of unique (and important) doctrines?