he also believed that Lut was a good man to give up his daughters to angel rapists
Can you give me a source for that?
I don't know much about Lut apart from the fact that his daughters slept with him.Try Wikipedia.

Here's the
wikipedia article on Lot:There's no father daughter incest in the Quranic version of it, certainly a point in the Quranic version's favor.

Main article: Islamic view of Lot
Jews and Christians do not consider Lot a prophet, but Muslims do. The story of Lot impregnating his daughters while drunk (Genesis 19:30-36) is not mentioned in the Qur'an and is considered a lie. The Qur'an does say that the people of Lot insisted on their wickedness of homosexuality, murder and robbery while also refusing to stay lawful to their wives.
And his people came to him, rushed on towards him, and already they did evil deeds. He said: O my people! these are my daughters-- they are purer for you, so guard against God and do not disgrace me with regard to my guests; is there not among you one right-minded man?
They said: Certainly you know that we have no claim on your daughters, and most surely you know what we desire.
He said: Ah! that I had power to suppress you, rather I shall have recourse to a strong support.
They said: O Lut! we are the messengers of your Lord; they shall by no means reach you; so remove your followers in a part of the night-- and let none of you turn back-- except your wife, for surely whatsoever befalls them shall befall her; surely their appointed time is the morning; is not the morning nigh?
So when Our decree came to pass, We turned them upside down and rained down upon them stones, of what had been decreed, one after another.[Qur'an 11:78]
And Lut when he said to his people: What! do you commit an indecency which any one in the world has not done before you?
Most surely you come to males in lust besides females; nay you are an extravagant people.
And the answer of his people was no other than that they said: Turn them out of your town, surely they are a people who seek to purify.
So We delivered him and his followers, except his wife; she was of those who remained behind.
And We rained upon them a rain; consider then what was the end of the guilty.[Qur'an 7:80].
Consequently, an Arabic expression for homosexuals is derived from the name for the people of Lot or Lut (in Arabic).i.e., Luti.
There's no criticism of Lot's action in giving his girls', he's even elevated to Prophethood, although he's not shown sleeping with them.
Because a lot of Muslims are ignorant of the fact that the Old Testament is fully accepted by Muslims. Those that aren't will just say they have know way of knowing if the Old Testament has been altered, much so like the rest of Chrisitianity. In any case there is more than enough crap in the Quran & hadith, so you do not really need to look much further.
Yeah, that makes most sense.

Peru - that's in the OT, Genesis.
Rashna- It could be because Islam and Mormonism don't rely on the OT as much as 'regular' Christianity does. Both Islam and Mormonism claim the former scriptures were corrupted, so they don't really factor into the 'new/perfect/correct' scripture.
But even "regular" Christianity doesn't rely particularly on the OT & never did-except for stuff like witches in the past, or gays today.
Right at the beginning circumcision was abolished, Jewish dietary rules were gone, unilateral male repudiation through a get was abolished, so was stoning & a Trinity along with a near deification of the Virgin Mary was the new faith's basics.
The OT was kept, but supposed to be superceded by Christ.
Also, even if some stories from the OT are explicitly included, Allah isn't blamed for say the murder of innocents in the OT period, like the Judoe Christian God is. At least, thats' how I have seen criticisms.