Actualy he was not. That's an urban legend. Here's his biography at the Museum of Broadcast Communications As you can see he was not yet 18, when WW-II ended. He was a college student from '46 to '51, and went to work 1951-53; program planner, producer, writer, and performer at noncommercial station WQED in Pittsburgh, 1953-62; producer and television host for the Canadian Broadcasting Company in Toronto, Ontario, 1962-64; producer and host of PBS show Mister Rogers' Neighborhood since 1967; So that rules out service in both Korea and Vietnam. No mention of any military service in that biography.
Lots of other sources confirm.
But...but...but...Captain Kangaroo raised the flag at Iwo Jima and saved Lee Marvin's life during fierce combat! And Mr. Rogers was a Navy Seal who wore those sweaters to cover the tatoos on his arms and muscular biceps!
Oh yes, and Obama is 100% qualified to serve as US President.
/s <- as if it's really necessary