Do you have to be Mormon to get into heaven?

I posted a response to a comment on the blog Mormon Matters about the topic Does the LDS Church claim to be “an exclusive conduit to God”?

Matthew Chapman said:

"Just a quick point of perspective. The vast majority of vicarious work will not be performed by “Mormons” - it will occur during the millenium, at which time “The Church of Jesus Christ of Latter-day Saints” must technically cease to exist as an organization. After all, by that time the “Latter Days” will be over and done with."

Growing up in the church I was never taught the church as an organization would go away during the millennium but that Christ would rule his kingdom/church personally on the earth.

"Brigham Young taught that there will be nonmembers of The Church of Jesus Christ of Latter-day Saints living on earth as well as members. There will be two great works for members of the Church during the Millennium: temple work and missionary work" (Gospel Principles, Unit Nine: The Second Coming of Jesus Christ, 44: The Millennium, 282)

Why do Mormons bristle when Evangelicals say that LDS believe that you have to be baptized a Mormon to get into heaven? The prayer for the proxy confirmation following vicarious baptism specifically confirms the dead as members of the Church of Jesus Christ of Latter-day Saints.