They are holding a joint debate at the Labour Party conference next week to exchange views on how extremism can be dealt with. They will also be asking if and how extremists can be brought back into the mainstream.
Although the two organisations are in many respects polar opposites, they are hoping their respective experiences will provide new answers on how to handle the problem of extremism in their different spheres.
"We thought it would be very interesting to get cross-fertilisation and see how people in the Muslim Council, who are part of the Muslim community but who are also not extremists, feel about and respond to extremism," said Alistair Currie, campaigns director at the BUAV, who will be speaking at the event.
It will be the first time the BUAV has attended a party conference and it is hoping the debate will help debunk some of the myths about the animal rights movement.
"People talk about it as if it's either a load of nutters or a core part of what animal rights is all about," said Currie. "Neither of those things is strictly true."
Dr Mohammed Abdul Bari, secretary general of the Muslim Council of Britain, will also speak at the event on 23 September along with Detective Chief Superintendent David Tucker from the Association of Chief Police Officers.