Yes you should be worried! Assuming your tractor is solidly built with hardware cloth and not chicken wire? You can make a hardware cloth apron around it which can be lifted up when you want to move it. Multiple threads on this forum describing how to do that in detail.
First, I don't see a pix of your tractor. If you have both predators active in your area, of course you have legitimate concerns.
A raccoon would pretty much take an easier route, of reaching inside and grabbing thru the wire, if he could reach/fit paw.
A coyote,,,,,,, well if very hungry, would attempt to dig possibly, but I think they prefer to find their meals where they can jump over a fence easier.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,and,
Should I be worried something crawling under a chicken tractor?
Of course it depends on what your tractor looks like and how uneven the ground is. Some critters like raccoons, possum, skunks, and especially weasels can squeeze through a very small hole under your tractor wall without even digging. It doesn't take some critters long to do some digging. I once watched a skunk digging a den about 25 feet from my coop one morning during daylight. It's amazing how fast they can dig. I did shoot it.
Can critters squeeze or dig under your tractor? Yes they can. Will they? That depends a lot on luck. Sometimes you can go years without problems, sometimes you get wiped out almost immediately. I have an apron around my permanent run. Once in ten years I saw where something (probably fox or coyote) tried to dig under and hit the apron. The apron worked. What caused me to put the apron on was that I surprised a possum in the run before it did any damage. I saw it squeeze under the fence to get out, hardly slowed it down.