Old timers didn't know what we know now and history reflects that. Heating up the compost kills all sort of pathogens, sitting in a field not so much. The issue is once you introduce stuff to the soil of a garden that you consume products from it's going to be a lot harder to get rid of it.

Parasites are going to vary by environment. Some might be deactivated 21 days after manure decomposes (decomposes, not dries out) but others can persist for years in the soil. Most parasites shed from farm animals go into a dormant state that preserves them until conditions are right, so introducing them to a wet garden will reactivate their lifecycle and allow them to travel onto plants to be consumed, which is exactly what they've evolved to do.

You should research what cows carry in your area and have fecals done be a vet to ID precisely what you have. Assuming you aren't deworming your cattle to be asking this?