Leaving FWD.us has nothing to do with immigration. Zuck's political advocacy group FWD.us also funnels money to http://www.americansforaconservativedirection.com/ -- Which also advocates for the Keystone XL pipeline and more drilling etc. (And also the mostly DOA 'Gang-of-8' Republican plan for Immigration reform)
US politics is pretty cynical, but not quite cynical enough to blatantly play both sides like this.
I'm speculating here, but I think you're wrong and that this is exactly playing both sides. To me it looks like a quid pro quo arrangement where FWD.us helps a conservative cause (the pipeline) in exchange for cooperation for a immigration reform. Keep an eye on it. I'd expect to see some political grease applied to a liberal cause in the near future too. I think their game plan is to basically buy favors with senators until they've got enough votes to pass a law they actually care about.
US politics is pretty cynical, but not quite cynical enough to blatantly play both sides like this.