On the sidebar, I'm trying to get one field with the category view to show radio buttons rather than checkboxes (so only one value can be selected at any time).
I don't want to use a point slider because I want to be able to see the different options.
One workaround would be to define a Text Choice Variable which has the values of all the country names, and then write Subset formula so that only data for each country are displayed based on the user selection in the Sidebar Variable radio button list of countries. If you post a scrambled sample of your file we can see if that is feasible.
Omar - Yes, you can specify variables with Sidebar user interactions that include radio button choosers to change assumptions and scenarios, then include these variables as values with operators inside SUBSET functions to drive filtering.
Specifying Sidebar Category filtering options for a given filed/column to be mutually-exclusive (user can only pick one) with a radio-button type chooser is still in this Idea stage...expand on the idea and vote for it here.