Without trying to give a psak, here’s my 2 cents:
I think there’s a big difference between working out as a bodybuilder, and working out just for your health. If your goal is to have huge muscles so you look good, it’s probably not a great idea. If you’re just doing it to stay healthy, I’d say not only is it allowed, it’s admirable!
I remember the following happening to me when I was in yeshiva:
Across the street from Darchei, there is a public baseball field. On Fridays in the spring, we used to go there after seder ended to play some ball. One Friday, I had changed into a T-shirt and had my glove in my hand, and was walking out from the yeshiva campus towards the field. Rebbetzin Reisman (the wife of R’ Yaakov Reisman, from the Agudah of Long Island) who was picking up her children, stopped me and told me, “I’m so happy to see you going to play ball! My husband always says that yeshiva bachurim need to remember their health! They need to take some time to exercise, even if it means stopping to learn for a little bit! Your health is more important!”