It's normal for all species, humans included. We generally aren't carrying large loads of parasites, but that's not because not doing so is normal. It's because we put tremendous effort into getting rid of them. This is one of the theories for why human body temperature seems to have lowered since the measurement was standardized at 37 C.

There was a poem written about the phenomenon:

Big fleas have little fleas

upon their backs to bite 'em

And little fleas have lesser fleas

and so ad infinitum