This is big news here in SLC. In fact NPR interviewed a local reporter about it on the national broadcast this afternoon. He said the initial reaction among local members is relief just as you have described. Others are even more angry, though, as it appears the leaders are citing modern revelation as the reason for the change in policy, and have declined to apologize or to acknowledge that a mistake was made.
The change in policy means that children will be permitted to be baptized, but the church still regards homosexual unions (sexual relationships) as apostate and sinful, even though the church will not label homosexuals per se with those terms.