Douglas Fairbank Jr is a good example. but there are many others, such as Clark Gable, Jimmy Stewart, and David Niven. Gable was assigned to film units in action and was almost shot down on one mission. Stewart and Niven were in combat units and saw extensive action. Stewart eventually made it to the rank of Brigadier General in the USAF Reserve. (He was given an additional promotion to Major General on the retired list long after his retirement. His promotion to Brigadier General occurred in 1959 and was merit based).

Fairbanks was a second generation Hollywood actor who was a leading man in his own right. His father Douglas Fairbanks and step-mother Mary Pickford founded the movie studio United Artists.

He was commissioned as a Lieutenant in the US Naval Reserves at the start of the war. He was given a relatively safe staff position in England under Mountbatten early on, but became aware of operational concerns after a convoy he had been part of planning was decimated during its mission.

It was the aftermath of that that is of interest here. Fairbanks actually used his prominence to further military operations. Fairbanks was transferred back to the states where he immediately began lobbying for a unit dedicated to military deception operations. He was able to get meetings with officials high in the Navy hierarchy that would normally not be available to someone of his rank and position. He eventually convinced the officials that such a unit was needed. The unit called The Beach Jumpers was created and Fairbanks was assigned as its commander. That unit was used extensively in the latter part of WW2 and saw some heavy action. That unit existed under that name until the end of the Vietnam War. The unit does have active descendants to this day.

Source: A Hell of a War by Douglas Fairbanks Jr

As to the rest, a very large percentage of stars were drafted, but then put into PR roles. Ronald Reagan, for instance, spent the war doing films for the US army and bond promotions.