Many of the leading stars of the World War II era served in the military, some, such as Clark Gable and Jimmy Stewart, on the front lines. I suspect none of the present day crop of movie stars ever wore a military uniform in real life.
There have been left wingers and outright Communists in Hollywood from its inception. However, many prominent actors and even some superstars in pre-1960 Hollywood were staunch conservatives: Gary Cooper, Loretta Young, Adolph Menjou, John Wayne, Clark Gable, Walter Brennan, and Ward Bond to name a few. Unfortunately, those days are gone.
The only one who I've heard express any interest in serving was Bruce Willis, and he was turned down in the past few years because of his age.
Gary Sinise comes from a military family, he said, and does a lot of entertaining of the troops.
But yes, as you pointed out, none of the current crop has served, not that I can think of.