Shirtless picture on the academic page of a Ph.D. candidate seeking postdoc
First, there is no rule that you need to have a picture of yourself on your professional webpage.  Most people do, but there's no rule.  It's nice to have some image that represents you (giving people's visual memories something to hold onto), but that could as easily be something from your research or anything, really.

Second, I would not recommend posting an image of yourself shirtless.  Your page will be looked at by (hopefully) a lot of different people with radically differing cultural and personal backgrounds.  Many of them are likely to have no problem with it, but some may.  When you are in an early and vulnerable stage of your career, it is generally safer to choose a relatively conservative image. Please note that I am not saying: "You Must Conform!"---instead, I am saying that failing to conform can have a cost, and that you should choose whether paying such as cost is worth it to you.

Finally, there is a simple solution that will nullify the question of being shirtless: just crop the picture to zoom in on just your face.