You could try granting permission in advance using the Page Info dialog. While you are on a Facebook page, you can call that up using either:

• Command+i (for Windows, Ctrl+i)
• (menu bar) Tools > Page Info
• click the lock icon in the address bar, then ">", then "More Information"

When the dialog comes up, click the Permission icon at the top to show that panel.

Camera and Microphone

Scroll down to "Use the camera" and uncheck the "Use default" box, and then select "Allow"

Repeat with "Use the microphone"

Any improvement?

See also:

• https://support.mozilla.org/en-US/kb/firefox-page-info-window
• https://support.mozilla.org/en-US/kb/how-manage-your-camera-and-microphone-permissions

I did do as you suggested using Firefox, but just got "waiting for camera" again. When I logged in with Chrome, it worked instantly! thanks for the tip!

Have you had luck with other sites accessing your camera, Facebook is the only problem so far?

(Mozilla had a page you could test with, but it's not loading at the moment. For future reference: https://mdn-samples.mozilla.org/s/webrtc-capturestill/; about this page: https://developer.mozilla.org/en-US/docs/Web/API/WebRTC_API/Taking_still_photos )

I'm remembering that MacOS has its own centralized controls on apps accessing the camera, so you might need to check those, too:

https://support.apple.com/guide/mac-help/control-access-to-your-camera-on-mac-mchlf6d108da/10.14/mac/10.14