Of course they are still in style! They're an absolute basic. From my point of view it's like asking if shirts are still in style. However, even though I seriously doubt that there will ever be a time when ALL shirtdresses are out of style, obviously there are some that are stylish and some that aren't. Shirtdresses are great for any age group, so much so that you can usually afford to get a very modern color and style and still not look inappropriate. They tend to be a very safe choice in general, assuming you know which style suits you. Usually when I see a dowdy shirtdress, the same three things are wrong with it: it's tea length, has a very full skirt, and has three quarter or full length sleeves. There's nothing wrong with any of these details individually, and it's possible to find a good shirtdress with all three, but this silhouette is extremely 1950's. Just imagine yourself wearing it with a strand of pearls and short heels. You would run the risk of looking like you just one the state fair's pie baking contest. I have a figure well suited to this kind of dress and I've made that mistake before. In general, a shirtdress with a slim, a-line, knee-length skirt portion, and a well tailored, close-fitting top portion should be flattering for most people. Also peter pan collars are running amok in shirtdress right now, and there a big no-no for most people, but other than that, choosing a lapel and shoulder line that is not typical of a basic button-up shirt will modernize the dress. I like to get a tuxedo style top portion, with puff sleeves and no colla, but it won't work for everyone. Try pairing it with a belt too.
It really works well as fun, feminine work wear if you know what your doing.