It's pronounced Gif, with a soft G as in Graphics.
I don't give a fuck what the idiot creator thinks it should be pronounced as, I'll die on this hill with my honor intact, surrounded by the corpses of everyone who thinks Jif is referring to anything but peanut butter.
It's pronounced GIF (sounding out each letter), like in that 'If Google Was A Guy' CollegeHumor video. Just so that it doesn't annoy or antagonise anyone for a meaningless purpose. Everyone wins.
Or, maybe both pronouncers (the "jiff" gang and the "giff" crowd) will team up against me for saying that. At least we'll have harmony for most people if that's the case, and I'll be a sacrifice to keep the peace.