First I've heard of it. I've been eating venison for years with no side effect other than a good case of gas! Someone mustn't have known what they were speaking of. Could be a PETA myth! Those are a different breed of folks.
The only reasonably common parasite in whitetail deer (dunno about mule deer) is liver flukes. And, if you don't eat the liver, they're of no concern. And liver flukes only infect a small percentage of the population.