Alas, even though the butchery rack is semi-portable, you still can’t do full butchery without a table - which is decidedly not portable.
I just carry around the lumber to build a table on the spot when I find something I really want to butcher and just set up a temporary butchering station outside my tailgate, then deconstruct and pack it up when it is time to move on.
For the phase of game before I have a reliable vehicle, I’ll find a decent intersection and set up a semi-permanent butchering station there, and just lure back any fat zombies or other things I really want to butcher to that position and kill them on the spot so I don’t have to drag them - obviously not a convenient method for butchering non-hostile animals however, and you need to be a good enough fighter to be able to take reasonable control over a couple blocks of your current town.