vanilla quake never compensated for non-square pixels (favouring 320*200 over 320*240 when both had the same physical display size on any monitor), so the only 'compatibility' thing is to keep the fov specify the major axis and have the other axis determined as a function of that. Whether you determine the major axis based upon 1:1, 4:3, or 16:10, or whatever the heck it is with the hud chopped out of it too, is up to you. Whichever you pick will mess up the viewmodel in some configuration.

For any ratio other than 1:1, you calculate the vertical fov as what it would be if your ratio were current, then calculate the horizontal fov as a function of that. Tall screens will then see much less, but also much less floor too.
Enabling dynamic window resizing first can really help with testing this stuff.
Make sure you properly recalculate fov aspect *after* everything else has been resized, and based only upon the view area's dimensions.