The suggestion is not to fly on United Airlines, but rather to use UA miles for flights operated by other Star Alliance carriers.
Transferring UR points to Hyatt for an award stay will have no effect whatsoever on your relationship with Marriott/Starwood.
I don't travel internationally, just domestically.
Using spend on Hyatt when it could be going towards Starwood Points doesn't make sense either (at least I think). You do make a good point about possible Starwood changes but I haven't been able to find solid information about what the rumors/leaked information is.
At that point I may look into Hyatt instead of Starwood.