I just needed to rearrange the categories in a Direct Publisher channel and I went through 5 browsers before I got to one that would actually work!
Firefox (56), SeaMonkey (2.48), Internet Explorer (11.674.15063.0/update version 11.0.47), and Edge (40.15063.674.0) DO NOT WORK!
Only Chrome worked. At the very LEAST you need to put that information (that you MUST use Chrome) on the page.
What really needs to happen is to FIX it. I'm pretty sure I used Firefox just fine before.
When you "hover over" the category and try to use the middle "button" at the top right corner the 4-way arrow indicator appears OK in the other browsers, but trying to drag the category to another location does absolutely nothing.