While the browser is listed in the default browser lists. It doesn't open correctly when clicking on a external link from another applications (at least in some circumstances).
This is because in the /usr/share/applications/mullvad-browser.desktop file, for the entry Exec, there should be an additional %U parameter to forward correctly the clicked link.
The full desktop file would read as follow:
[Desktop Entry]Version=1.0Type=ApplicationName=Mullvad BrowserGenericName=Web BrowserComment=Mullvad Browser is a privacy-focused web browser designed to minimize tracking and fingerprinting.Categories=Network;WebBrowser;Exec=/usr/lib/mullvad-browser/start-mullvad-browser --detach %UIcon=mullvad-browserStartupWMClass=Mullvad BrowserMimeType=text/html;text/xml;application/xhtml_xml;x-scheme-handler/http;x-scheme-handler/https;Terminal=false