It's not the OP that irritated me Queen it was some of your post, I'll explain what I meant (apologies for the numbering, it just helps me):
1. Tell your Brother you won't be going to the wedding because you are the one who will have to deal with a girlfriend who would be humiliated if you went alone.
The girlfriend would not be humiliated by her partner either attending the wedding alone or not going at all. It's a family wedding and presumably, the girlfriend would not want to lay down the law for that reason. Well, I wouldn't - I might be a bit hurt and I might urge my girlfriend to really sort this crap out with her mother but, make a fuss on my brother's wedding day? Not on your nelly.
2. And tell him to make sure that he tells his friends the reason you are not there is because he didn't invite your girlfriend.
Another instruction for the brother. Why does he have to tell his friends anything on his wedding day? OP has access presumably to all of the guests, including family, and can do so herself.
3. Also tell him that you expect he will have a bit of bridge building with your partner., you wouldn't blame her if she chose not to have anything to do with him.
Yet another instruction for the brother. Anybody telling me that I have 'bridge building' to do for fear of the girlfriend not forgiving him, thereby coming between brother and sister would find themselves very much outside my circle of family, I wouldn't put up with that. You sound like you're stirring it actually, Queen.
4. To conclude, Put your partner first and I am really sorry about your brothers reaction.
Why? It's OP's brother's wedding day, presumably his only one and the most important day of his life. OP can easily sort this out herself with her mother and family (and, at time of this post, actually has done so).
5. You must be very hurt that he is enabling your mother. Think of the coolest lesbian and imagine her in this situation... What would she do?
Urgh... coolest lesbian? How about fully-grown adult and functioning feminist instead? OP has also been enabling her mother and, if you accept that she's been 'under the cosh' for many year you must also concede that for her brother.
You've completely ignored all reference to the mother's bigoted and disgusting behaviour in your post and I said your post was selfish because you rode roughshod over OP's brother's wedding day... all OP had to do was 'come out' to her family and this she has now done. "Go OP!!"