Always try using your device's web browser (which always honors Android proxy settings) to see if you are still able to access things.

Specific apps that are known to have issues are as follows:

Stuff like games and some streaming services will use UDP and thus not work.

Weirdly enough, you can SEND messages, you just can't RECEIVE any.

What does seem to work though is using Messenger on a proxy through a mobile web browser (which always honors the Android Proxy settings), and using the Desktop version of the mobile website. Weird - but for now it seems to at least be one way to use Messenger on a phone via a proxy connection