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tl;dr I'm a little stoned and trying to make a coherent argument
You got really close!

I can't speak for other Abrahamic religions because I honestly haven't had enough exposure to them. You are right about Christianity being one of those that you can't 100% though. Any Christian who claims they are would be a liar, even if they're only trying to live up to the current standards of what it means to be "Christian."
I don't see the majority of the Christian community changing their views on homosexuality any time soon though. The fabrics law was dated to the old testament, only mentioned once (to my knowledge), and I honestly don't know when views on that changed or why. For Christians, animal sacrifices went away after Jesus died. Attitudes towards women, in my opinion were severely misguided and taken out of context (One heavily used scripture was a letter written by Paul to one of the churches he watched over cautioning them not to let women teach in the church. In context though, it was because these women had came from a temple that worshipped another deity that promoted having sex on the alter and prostitution.). And as far as slavery goes, it's known that it existed even through the new testament times, but the only references I've seen to it talked about treating slaves kindly. I haven't actually read anything saying that it was a man's right to own a slave.
Homosexuality, or the "practice" thereof, on the other hand is something that is outright called a sin several times throughout the Christian bible. I think this is where the difference is made.
But the last thing this old duck dude was hired to do was to give his opinion on social issues. So it made sense for him to be fired and it was the public outrage at the supposed infringement on his freedom of speech that I find to be so wrong.
I agree with you on this completely. The argument that his freedom of speech was violated is completely ridiculous. A for-profit television company hired him to do a show, and they felt like his opinions expressed off the camera were against their best interests and that they might decrease viewership. They didn't put him in jail, and they never stopped him from saying what he wanted to say in that article, they simply suspended him from work. Yes, A & E knew what they were getting into when they signed him and the other members of his family on to do the show, but that is not the main reason they hired him.