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.
The Big Lebowski (for more Lebowski-oriented stuff): https://www.facebook.com/groups/Lebowskifans
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