You cannot put a bar chart on a map with Tableau, but now there is an alternative that can accomplish the same task for some applications. The view you see below was created by Vanya Tucherov and Raif Majeed, two of our resident dev-hero's, using Gantt bars instead of pie charts.
This must be complex, right? It's not! Just make your view as you normally would if you were going to use pies, then switch your mark type to Gantt. There you have it, bars on a map. This won't work perfectly for all applications, but it can be an interesting way to avoid pies on occasion.