We do not share parasites with cattle and chickens. We DO share parasites with pigs. I STILL cook my pork long enough to kill a tapeworm.
Here's the deal, a parasite needs a host to survive. The worm sheds eggs which leave the herbivore via the feces. Survival depends upon being eaten on the grass by another host herbivore. When it is dry, whether hot or cold, the eggs die. We horse owners try to remove their poo and pile it up, which heats the eggs and kills them. Droughts also kill them. Dewormers kill them best of all, but every horse still carries a small parasite load. Some are more resistant than others. Generally "hard keepers", horses that have a hard time keeping weight on, are less resistant to parasites, for the most part. I am NOT an expert on this, but the horse community has gone to have fecal samples tested for #'s of parasites. We don't deworm these horses as often as those with less resistance.
Point being, by the time you use cow manure the eggs are dead and you will not injest them.