The early followers of Jesus/Yehoshua called Paul "the enemy" after he fled to Damascus. From the Recognitions of Clement Chapter LXXI: Flight to Yericho
"...Then after three days one of the brothers came to us from Gamali-El, whom we mentioned before, bringing to us secret tidings that that enemy had received a commission from Kayafa, the Kohenha Gadol, Caiaphas the High Priest) that he should arrest all who believed in Y’shua, and should go to Dameshek (Damascus) with his letters, and that there also, employing the help of the unbelievers, he should make havoc among the faithful; and that he was hastening to Dameshek chiefly on this account, because he believed that Kefa (Peter) had fled thither..."
Muslims also don't accept Paul as a true apostle, even though they do accept Jesus/Yehoshua as the prophet of God that he claimed to be.
In this video linked to below, John suggests that the Islamic story of an angel who wouldn't come near a puppy is about animal nature / sin. Now, this makes so much sense. I wonder if all the times the word "dog" is used in their texts it refers to this, and there's no reason for them to hate dogs and call them all sorts of nasty names, because it was an allegory for animal nature. We see that those who sin are called Gentiles and they were called dogs in the bible. Those who go back to sin are compared to dogs returning to their vomit.
We see in the Clementine Homilies that if the woman who called herself a dog would have not become Hebrew (crossed over into KEEPING the commandments), then she would have still been considered a Gentile and still been considered a dog.
Clementine Homilies 2 Chapter XIX. Justa, a Proselyte "There is amongst us one Justa, a Syro-Phœnician, by race a Canaanite, whose daughter was oppressed with a grievous disease. And she came to our Lord, crying out, and entreating that He would heal her daughter. But He, being asked also by us, said, 'It is not lawful to heal the Gentiles, who are like to dogs on account of their using various meats and practices, while the table in the kingdom has been given to the sons of Israel.' But she, hearing this, and begging to partake like a dog of the crumbs that fall from this table, having changed what she was, by living like the sons of the kingdom, she obtained healing for her daughter, as she asked. For she being a Gentile, and remaining in the same course of life, He would not have healed had she remained a Gentile, on account of its not being lawful to heal her as a Gentile."
So, this may be another similarity between Islam and the early followers of Yehoshua.
John says that even though the leaven is the same allegory we see people taking it literally. So in Judaism people make sure to have no leaven in their houses literally, and in Islam they make sure to have no dogs in their houses. But this isn't a literal thing, it's symbolism for getting rid of sin/false doctrines/animal nature etc so that our houses (our bodies are our temples) can allow the Holy Spirit of YHWH inside.