I don't think anyone is claiming that Group A actually can kill everyone they oppose. The problem is that they want to, and that they are trying to, and that before all is said and done, they will have done so to many innocent people.
Also, you are guilty of what you accuse Group B of being guilty of. I don't see anyone in Group B claiming that all of Group A is responsible for "all of the world's evils." If the OP made that claim, then I don't consider him part of Group B. Put him in his own, grossly exaggerating group.
No, the Group B I'm talking about is the one simply pointing out the explicit goals and actions of Group A, and its association with a certain religion. The Group B I'm talking about does not claim that all members of that religion are members of Group A.
All this "group this" and "group that" is getting a bit tiresome, but on the other hand, I think it's very important to speak precisely when dealing with issues like this. Once you begin lumping people together, generalizing and stereotyping, meaningful communication breaks down, and fighting starts. And fighting is the problem we're trying to solve here.
I'm not familiar with Britain First, so I don't know why you call them despicable. But I have read about Muslim gangs which have been getting away with child sex slavery in UK cities since at least 1988. This is documented in major UK and international newspapers. I wish you would also call out those groups as despicable. Note: I didn't say that all Muslims are despicable. Anyone doing those things to children is despicable, regardless of their religion.
I don't know what the OP said, since it's hidden. But I would caution you against playing the "bigotry", "narrow-minded", and "hatred" cards. They are too easily used by one side to silence discussion of apparently unpopular opinions. There are bigots on both sides of the issue, but not everyone on one side of it is.