Not that I recommend this for all boots, but I have tossed some in my washer before. I've done muck boots that were forgotten in the garage and paddock boots...knowing I might destroy them in the process and accepting that risk. Front loader, cold water, mild soap. So far, no casualties!
I know the boots you're talking about as I have gone through several pairs over the last few years. Wipe the mud off with a damp rag and then use some Horseman's One Step on them to put the shine back on. That material is weird (and cracks easily).
Dish soap and warm water. Scrub gently--I used an old dish brush that will never see dishes again--then water to rinse, and air dry. I didn't douse them, but I did get enough water inside the boot from my shower spray that I let them air dry for a good three days.
I'm 5+ year wearer of the Mountain Horse Ice Rider paddocks, and saver of my trainer's Mountain Horse Ice Rider tall boots that she thought had become too disgraceful to wear in the hunt field. One good washing and two new zippers later, and her boots are still in use over a year later. She did manage to grind the dirt into the inside heels and I couldn't get that out, but since it's facing the horse when she's mounted, nobody really cares. I assume if she'd started tending to her boots a little earlier--like, ever done more than just hose them off--even that could have been prevented.