Ed Greshko:
>> xdg-settings get default-web-browser

Kevin Cummings:
> For me it returns: "xdg-settings: unknown desktop environment"
>
> B^)  I run MATE desktops.

Likewise, on both counts.  While I don't use Thunderbird, other things
do open the right web browser (for my personally set preference).  And
for further information, just following up on something later on in the
thread:

[tim@fluffy ~]$ xdg-settings get default-web-browser
xdg-settings: unknown desktop environment

[tim@fluffy ~]$ xdg-settings get default-url-scheme-handler
xdg-settings: unknown desktop environment

[tim@fluffy ~]$ xdg-settings get default-url-scheme-handler
xdg-settings: unknown desktop environment