Parse error when installing any application

I cannot install any F-Droid applications anymore. I've been using it without issues for years, but now whenever I try to install an application, I get a "Parse error - There was a problem parsing the package" message, followed by a "(De-)Installation Error" message.

I tried freeing up extra space in my phone, and also uninstalling, re-downloading and reinstalling F-Droid, to no avail.