So we can add custom fields to our schematic by Tools>Edit Symbol Fields. But rather than text is it possible to add checkbox fields, like the Exclude or DNP fields? Or are those field types hard-coded into the application?
I know I can just populate with “Y” “N” “0” “1” etc, but checkboxes are just nicer.
(Using v9.02 on Windows)
Sure. The DNP field is apparently default visible in my KiCad V8.0.9 (do mind the extra dot please). To change the visible columns, just right click on the first line with the titles (what’s the name of that thing?) and a context menu with all possible column names pops up.
Sorry 9.0.2 
What I meant is: I can add a field, but it’s always a text field. I would like to add my own checkbox fields.
That makes it a completely different question. Schematic Editor / Tools / Edit Symbol Fields just modifies the values of existing fields. It does not add fields. If you want to add fields, you have to modify one of the symbols. (Either modify via the properties in the schematic editor, or in the symbol editor).
As far as I know, there is no option to add checkboxes at the moment, but only text strings. The option to add checkboxes may be worth a feature request on gitlab. When you want to make a feature request, first search though the existing issues, there are over 1500 open issues (bugs and fearure requests) on gitlab.