My uncles ex-wife does not like his family anymore post divorce. Is this normal after a divorce?

Yes this is very normal and it is called post divorce.   

Maybe she never liked anyone on his side of the family anyway 

She's the one who requested the divorce, and now she's mad because your aunt wants to know your uncle's new girlfriend?  It sounds as if she's very childish.  If she refuses to have anything to do with his family members, then it's her choice.   Write her off as a past memory and embrace the new relationship.  I hope it's happier.

Heck people happily married often dislike their in-laws.

It's cliche'. 

On the other hand my brother's father-in-law allows his wife's ex to come by and watch football games with the family and doesn't seem to mind at all... a real easygoing guy and I think maybe that's his way to eliminate stigmas or taboo things... by bringing them out in the open.

There is absolutely no threat to the marriage when he is there - as far as I see it.

I didn't even know who he was and assumed he was the guy's brother since they resemble each other in all irony. 

What am I not understanding here: the aunt "requested the divorce"? I don't get it. Its up to the couple in question, not an "aunt". If someone doesn't like a relative post divorce, chances are good they didn't like the person before then, but kept it more to themselves, unless the person did something horrible for which to be disliked. . 

Yes.