Is there a way in the free CartoDB to set the layer selector so that you can only select 1 layer at a time? When one layer is selected, deselect all other layers.
There is currently no way to do that in that actual editor, however it is possible using CartoDB.js.
There are multiple ways to do this with CartoDB.js, take a look at the following two examples:
The first one hides the other layers and only allows one to be visible at a time, however, it is very easy to modify the second one (using the CartoDB.js API methods .hide() and .show()) to get the functionality you want.
Check out the CartoDB.js documentation for more info on the .hide() and .show() methods.
One more thing, the second example uses named maps, which only apply to private data sets, so just use it as a guide for how it uses the .toggle() method to hide and show layers.