Facebook I hate cyclists group infiltrated!

Nice work fellas. As many of us as possible should send a request to join this group and let our feelings be known!!!
I would have thought it's much better to report the group to FB mods. You can't argue with people like these (although yes, some of the comments on that page make me want to weep) and by getting in to a debate with them you're only going to raise their group's profile and rile them further.

Seriously, write to their employer if you wish but then walk away.