You can definitely set up action filters based on custom shapes (which in your case will be your picture of a boy or a girl). This article from Ryan Sleeper outlines how to do it:
Edit: Having looked at it in some more depth it isn't quite what I was hoping for. Would it be possible instead of just changing the numbers, actually bringing in a whole new chart from different sheets each time you click a selection?
Looks promising. Going to give this one a crack. Thanks Paul
Hi Steven, we have already published a few vizzes using icons or pictures as navigation, but I want to alert you to the latest version of Tableau 2018.3 - its got navigation buttons !
You can OFC customise your navigation button to be a picture but the benefit of this is it doesn't leave the trace 'selected' mark which was a consequence of the old solution.