I have read that a very high percentage of members of the LDS church today are first-generation. Recently I had the following experience with one of them:

About two months ago I sat at a restaurant with a college student who had grown up Mormon as she recounted to me her growing doubts about Mormonism. I shared that when I was an LDS college student, I also had to make some decisions about Mormonism. But things were very different, because the Church’s doctrines had changed so much – what with the ban on black men in the priesthood, the fact that all American Indians were no longer considered Lamanites…

Her face went completely blank. “What do you mean, about blacks and priesthood?”

She had grown up her whole life a Mormon and never knew.  — (from The Mormon Mirage 3rd Edition:  A Former Member Looks at the Mormon Church Today(Zondervan, 2009). Also available as an audiobook and as an expanded-text E-book for Nook, Kindle and other reading devices.

Here is an excellent online source for some of the LDS church's past teachings on race.