According to "Us Weekly", TAYLOR SWIFT and CARRIE UNDERWOOD "hate each other" . . . and ordered Grammy execs to keep them separated at Sunday's show.  Another source said, quote, "Taylor feels Carrie is always rude to her, so she steers clear of her."However, Gossip.com found a friend of Taylor's who claims it's "100 percent untrue."  Also . . . Taylor just found out last week that she's the opening act.