From what I can see the "hate group" has been set up because cyclists ride in the road rather than using cycle paths, which from the point of view of a non cyclist can be pretty confusing and annoying, rather than just bitching about it why not spend your time and effort trying to get cycle paths improved so that more people use them and the public image of cycling is improved.
Also facebook groups are only good for getting old bands to number 1 and then that wasn't really that impressive, if you don't like it just ignore it and there will be a new and different "hate group" next week.