Why does the LDS support it?
My understanding is that the LDS church opposes Gay-Marriage, but does not support discrimination against anyone, for any reason.
...two new laws that create protections against discrimination based on sexual orientation or gender identity.
Everyone has to live somewhere, these laws simply said that you could not deny a person the right to live in a home or apartment (that they can afford) simply because they are gay or transgendered. You cannot deny this basic right to Blacks, (no black-free apartment complex) or people with children (single-only apartments); now you cannot have either an gay-only or gay-free apartment complex.
Devil's in the details. Religious organizations are exempt from these laws.
(I think it's a reaction to the negative Prop 8 stuff the homosexual activists have been putting out...ya gotta understand that the Lds general authorities are largely businessmen who tend to try to be PR "savvy"...so they sought to try to counter what they perceived as "negative" PR with "positive" PR...the problem is, what the LDS church did in CA was "positive"--not negative...now they're running the wrong way)