I'll try to answer your questions as best I can. Don't worry about offending me by asking religious questions. I'll try not to give you the gospel according to Puff, since I'm a sample of one.
This might help a bit for some background.
From our Articles of Faith - a list of basic tenets of our faith.
11. We claim the privilege of worshiping Almighty God according to the dictates of our own conscience, and allow all men the same privilege, let them worship how, where, or what they may.
12. We believe in being subject to kings, presidents, rulers, and magistrates, in obeying, honoring, and sustaining the law.
And this statement issued by the LDS Newsroom on December 8, 2015. This was issued just one day after Trump's "Muslim no fly" comments.
The Church of Jesus Christ of Latter-day Saints is neutral in regard to party politics and election campaigns. However, it is not neutral in relation to religious freedom. The following statements by Joseph Smith from 1841 and 1843 are consistent with the Church’s position today:
If it has been demonstrated that I have been willing to die for a "Mormon," I am bold to declare before Heaven that I am just as ready to die in defending the rights of a Presbyterian, a Baptist, or a good man of any denomination; for the same principle which would trample upon the rights of the Latter-day Saints would trample upon the rights of the Roman Catholics, or of any other denomination who may be unpopular and too weak to defend themselves. It is a love of liberty which inspires my soul — civil and religious liberty to the whole of the human race.
—Joseph Smith, 1843
Be it ordained by the City Council of the City of Nauvoo, that the Catholics, Presbyterians, Methodists, Baptists, Latter-day Saints, Quakers, Episcopals, Universalists, Unitarians, Mohammedans [Muslims], and all other religious sects and denominations whatever, shall have free toleration, and equal privileges in this city ...
—Ordinance in Relation to Religious Societies, City of Nauvoo, [Illinois] headquarters of The Church of Jesus Christ of Latter-day Saints, March 1, 1841
Just guessing here, but Milo is from the UK. If we look at Europe, I'd guess that people are concerned about high rates of immigration along with relatively high birth rates among Muslims flipping this rather quickly. Since the Orlando shooter targeted gay people, I can see reason for that group to have some fear.
I mentioned a Pew Poll on Muslim beliefs earlier. This might be helpful if you're looking to compare and contrast LDS views. I find much of these attitudes very concerning. Look at the numbers of people who support Sharia law for non-muslims, or who support execution for people who leave their faith tradition, or who support stoning for other offenses.
Me too, and I haven't seen the poll he was referring to.
Please take a minute to read our official statement here, before reading my opinions about some of the politics of it.
Let me give you a little history regarding the politics of this, and my opinion. The church supported "Marriage between a man and a woman," while supporting civil unions and all rights that would go along with that. That position would look more like what was going on in the UK where Milo is from, or what Elton John proposed at the time. The LDS church took issue with the word "marriage" specifically, but is opposed to any discrimination. Utah has been a leader among the states to pass LGBT anti-discrimination laws. When CA passed Prop 22 in 2000, 61.4% of the state supported it. A broad coalition of churches including the Catholics, and other evangelical and protestant groups supported traditional marriage. A majority of Black and Hispanic voters supported Prop 22. There was a similar situation with Prop 8, in 2008 but by that time support for gay marriage had begun to rise, so it only passed with 52.47% of the vote. Again, there was a broad coalition of different religious groups who supported Prop 8.
The LDS church was a target for the left on this issue, in part because we're a young, centrally organized church that they view as predominantly White and Republican (That is shifting very rapidly on both fronts, but that's another story.) AND We're more organized than many other religions in terms of quickly bringing humanitarian aid to hurricane ravaged Baton Rouge, and we're also more organized and effective in mobilizing on moral issues like state-sponsored gambling or the definition of marriage. Also, it's far less risky to say, "Look, the Mormons hate gays." What do Dems have to loose in that? It's far more risky to say, "Look the Catholics and more religious Jews, and Evangelicals, and Black people, and Hispanics hate gays." Nobody wants to alienate their voters, right? Also, remember what was going on in the Democratic party and statements both Obama and Clinton made about gay marriage back in the late 90s or early 2000s.
There's a hypocrisy among progressives in terms of protecting some groups and not protecting others. I think you know I support free speech here, so don't imagine that I think it's a big problem if someone tells a Mormon, Catholic, Jew joke. BUT it's a little weird for the secular left to think it's perfectly fine to have a musical that mocks my beliefs, and award it a a bunch of Emmy awards. Zero LDS people opened fire in the theater, but we are to refrain from drawing a cartoon or saying anything that is offensive to Muslims. If you bring down the wrath of some jihadist, then you probably "had it coming."