I have not been around the mud much but mine cleans up like new by easing it with Eagle One Nanowash & Wax. Then when wiping it down I spray on Eagle One Wax As-U-Dry. And for touch up after I was Eagle One Wipe & Shine. And on the wheels I use the Eagle One Wheel & Tire Cleaner (This makes the wheels just look new without the shine).
I have had good luck with Eagle One products and I would guess other brands are just as good. But the Wax As-You-Dry might be what you are looking for or something like it.
What LBR used on all his black plastics & roll bar is by turtle wax and it's called black wax I bought it years ago for our softops on our jeeps...when I went online to see if they still made it it's now called "back to black"