Our main Dudeism page is https://facebook.com/Dudeism.
Our main Facebook group is https://facebook.com/groups/duderino. Note that this group is mostly for stuff about Dudeism. Not really a place just to post Lebowski memes. Also, no political stuff is allowed. Read the rules at the top of the page in the pinned post.
Lebowski.org (for more Lebowski-oriented stuff): https://www.facebook.com/groups/lebowski.org/
The Church of the Latter-Day Dude: (a smaller and more permissive group): https://www.facebook.com/groups/Dudeist/
Dudeocracy: https://www.facebook.com/groups/dudeocracy/ (for political stuff)
Twitter page: https://twitter.com/dudeisms