The ability to synchronize sheets in Tableau Desktop is still a feature request for the product. There are a few different ideas that I think you should vote on to show support for them to be added to the future versions of Tableau.
This thread is a similar request for zooming multiple sheets at a time, in this thread they are maps, not charts: zoom together multiple maps of a dashboard
Hope this helps!
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Since the ability to synchronise sheets is not yet implemented, you can use Parameter + Calculated field to toggle between day and month.
Not a perfect solution but solves the purpose.