I suspect that the who methane (CH4) production from refrigeration worldwide is a rather small fraction of that generated by dairy cattle and other ruminants. We could of course kill off all the ruminants and go over to pulse-based diets, but I suspect that methane generated by human digstion would then outweigh that arising from refrigenration.

And you should remember that certain gasses formerly widely used in refrigeration but now banned reduced warming (they damaged the ozonelayer).

Also, It would not be unreasonable to suggest that controversy about man-driven global warming might have been less if (a) the advocates acted in good faith, instead of attempting to conceal their data sources and (b) they managed to produce accurate predictions of future things, instead of merely being able to juggle parameters in their models to better fit past things. Maybe climate science hasn't abandoned teh science method to quite the extent that string theory has, but some of its practitioners have come pretty close.