I had something similar to your needs. I'll show you how I "solved" it:
-I created a handful of dashboards for one "team" and started there.
-Instead of starting from scratch I used the "Replace Data Source" option and put in the corresponding teams data to the dashboard.
-So Now I've created the dashboards For each team and all I have to do is change the colors around and maybe a few pictures.
-Then I let Tableau server/Online do all of the work. I published each dashboard and the corresponding data set to the server and used a data extract every day to keep the data fresh for each separate team.
It seemed tedious- but it didn't take more than half a day. For the use case I was on, the benefits of Tableau were too great to pass up on so we went with a slightly more complicated approach.
Hope that helps!
Thanks for the suggestion - we will definitely consider that as one option.
I have also been shown that certain colors and elements can be controlled by calculations and shapes, based on the users group, so that may be another option for us. The main issue about that approach is that you would only be able to set one color in the palette, so in a bar chart I could have every bar red for Team A and every bar blue for Team B, but I couldn't using a diverging red/blue color scheme, for example.