It is not possible to "export" your folder settings, but there is a feature that allows you to save your folder (and other) settings as a custom settings file.
Classic UI:
When you have selected your folders, filters and other settings, go to the "Administration" tab.
New UI:
When you have selected your folders, filters and other settings, go to "Settings" under the "hamburger" menu on the top-left.
Click {Save As} in the Settings section. Save the settings using a file name of your choice.
This will save all your folder selections, filters and other settings that are active at the time you save the settings.
When you wish to use those folder selections and settings again later, simply click {Load} and select your saved settings file.