I'm having the same issue, so I will try to fix it later and get back to this post if any of these methods work.
EDIT:
I tried both methods. The Arch one did nothing, while the xdg-settings one did set Mullvad Browser as my default, but when I click a link the browser will open on the homepage anyways. So yeah, seems like we gotta wait for this to get fixed by the Mullvad devs.
I had tried that but Network Manager couldn't read the config or something. Anyways I fixed the issue by enabling quantum tunnel, but thank you anyways for replying!
This is an open issue on the Mullvad Browser GitHub.
One person in the thread who's using Pop OS posted this:
However they do report the clicked URL not being passed to the browser, so it doesn't seem to be that good of a solution.
This reply worked for someone on Arch though.
I'm having the same issue, so I will try to fix it later and get back to this post if any of these methods work.
EDIT: I tried both methods. The Arch one did nothing, while the xdg-settings one did set Mullvad Browser as my default, but when I click a link the browser will open on the homepage anyways. So yeah, seems like we gotta wait for this to get fixed by the Mullvad devs.