Unable to give access for app to use camera or microphone

I'm unable to grant access for an app (Slack) to use the camera and microphone. There are no + / –  buttons that I can use to manually add an app to the list of allowed apps, and Slack doesn't appear in the list.

This happens whether I navigate to System Preferences > Security & Privacy first, or whether I instigate the process from within the app itself (which lands me in the same place).

What can I do? This has never been an issue for me on previous MacBooks or earlier OS X versions. It's driving me nuts.