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(1) both feature a single prophet received a revelation from an angel

Christianity and Judism also have a prophet, and revelation from an angel, John the Baptist, and or Jesus Christ, and Moses, respectively.

(2) both had violent early histories (although Mormonism has become peaceful, while Islam has not)

Hmmm...Mormon history is violent at times, mobs against Mormons anyway!

(4) both have similar views on 'lifestyle' issues, like alcohol, etc.

You mention alcohol, but that is about the only item I can think of too. As we don't believe in smoking, but I don't think that is proscribed by Islam. I would think that Islam, Christianity and Judism all share many common lifestyle values.

(5) both are post-Christian creeds, with a written scripture that contradicts the New Testament

Well, at least you, and others, believe it contradicts the NT, but we believe the Book of Mormon is a Second Witness of Jesus Christ, and it explicitly witnesses that the OT and NT are divine in origin.

How does the politically conservative Mormon view Islam?

I can't speak for the faith, but being a member, I would think that Islam is an anti-Christ religion, i.e. they deny the divinity of Jesus Christ.

Both (Islam and Mormonism) feature a single prophet receiving a revelation from an angel.
Christianity and Judism also have a prophet, and revelation from an angel, John the Baptist, and or Jesus Christ, and Moses, respectively.

Judaism stands on the the testimony of numerous prophets, numerous visitations by angels, numerous visitations by God Himself, numerous miracles of God, numerous examples of fulfilled prophecy, a recorded history which is verifiable outside of it's own sources, and a collection of writings which are, again, verifiable by those outside of the system of belief.

Christianity adds to that with the incarnation of JESUS (God with us), more examples of fulfilled prophecy, the testimony of numerous apostles, a continuing history which is verifiable outside of it's own sources, and a collection of writings which are, once again, verifiable by those outside of the belief system.

The veracity of Judaism and Christianity rest upon a multitude of information sources.

On the other hand, the veracity of Islam and Mormonism each rest upon the testimony of one man and a few of his associates.