Strategic Air Command

Robert "Dutch" Holland (James Stewart) is a professional baseball player with the St. Louis Cardinals,[Note 1]. A B-29 bomber pilot during World War II, he is also an officer on inactive status in the United States Air Force Reserve. During spring training in St. Petersburg, Florida, he is recalled to active duty for 21 months. He reports to his posting at Carswell AFB, a bomber base in Fort Worth, Texas to qualify in the Convair B-36. He arrives in civilian clothing because his old uniforms are those of the old U.S. Army Air Forces, for which he is rebuked by General Hawkes (Frank Lovejoy), the commander of SAC. The General's character is patterned after the real SAC commander of the time, General Curtis LeMay.
Dutch is given a staff job with the bombardment wing at Carswell that involves a lot of flying. He soon has a B-36 crew of his own, selecting a former World War II colleague as his flight engineer, and becomes enamored with both flying and the role of SAC in deterring war. He is joined by his wife, Sally (June Allyson), who had not bargained on being an Air Force wife, and who struggles with his repeated absences and the dangers of flying. On any given night, Dutch might find his aircraft on airborne alert far from the continental United States, in secret, only telling his wife when he returns days later. Even so, Sally tells Dutch that she is happy as long as they can be together, no matter what he decides to do with his life.
The B-36 is a complex aircraft when introduced, but improvements are being worked on all the time. One challenge was leakage from the fuel tanks, but a new fix is introduced to address this once and for all. On their next flight, Dutch's crew has to fly their B-36 from Carswell AFB to Thule Air Base, Greenland. The fix does not work and one of the engines bursts into flame, causing the entire left wing to catch fire. The crew is forced to abandon the aircraft and bail out over the ice and snow of Greenland before arriving at Thule. Dutch and his Radar Navigator stay on board for a forced landing, which causes Dutch to injure his right arm.
Dutch becomes a favourite of General Hawkes and is rewarded with a revised assignment flying the new Boeing B-47 Stratojet at MacDill AFB in Tampa, Florida, across the bay from St. Petersburg where his old baseball team continues to conduct its spring training. Promoted to full "Bird" colonel and made deputy wing commander of his B-47 wing at MacDill, Dutch decides, to Sally's displeasure, to remain in the Air Force, rather than return to baseball at the end of his active duty obligation.
On a full B-47 wing movement exercise that involves flying nonstop from MacDill to Yokota Air Base, Japan, they encounter severe wind and storms. Low on fuel, they divert to Kadena Air Base, Okinawa. As they prepare to land, Dutch realizes that his arm injury from the B-36 crash was worse than he thought, and it is almost immobile. He is unable to operate the engine power levers (throttles) during final landing phase and has to rely on his co-pilot to do so while Dutch works the flight controls with his left arm and feet.
This injury not only bars him from further flying (he is discharged from the Air Force (USAF) shortly after the incident), but also appears to threaten his baseball career. General Hawkes suggests he would make an excellent team manager.

Question: What professional baseball team did Dutch play for?
Answer: St. Louis Cardinals