It's not just the update that did this, there's been some sort of change to YouTube itself that is causing this. Hopefully there will be an app update ASAP to resolve the issue. My unit has not been updated yet and YouTube is crashing on it as well.
Indeed, the YouTube app is working fine today for me as well. I could be mistaken, but YouTube is one of the apps that gets auto-updated on Android devices, is it not? I recall seeing it auto-update at least once on my SGS2, I believe on my Acer A500 as well... so either the app updated at some point in the last 24 hours or so, or whatever was changed on YouTube itself has been fixed.