Some calf diseases can transmit to people.  Any diseases that can transfer from animals to humans is called a zoonotic disease.  Dr Jeff Binder from the University of Minnesota says in Bovine Veterinarian that although dairy farmers have a unique affection for the animals they raise, kissing calves is not a good idea. 

According to the Centers for Disease Control and Prevention (CDC), in 2017 there were 59 outbreaks of zoonotic diseases that led to over 1500 reported illnesses in humans, over 300 hospitalizations, and three deaths.  And about two-thirds of these diseases were from livestock and poultry operations.  Certainly, you have a higher risk of getting these diseases if you live or work on a farm, as people were eight times more likely to get a zoonotic disease on the farm versus living in a non-farm area.  As far as calves are concerned, bacterial infection with Salmonella Heidelberg caused an outbreak in 2018 across 15 states and caused 56 human cases.  The disease in humans led to diarrhea, fever and stomach cramps.  Another disease called Campylobacter is highly infectious in children less than one year old and can cause severe diarrhea.  It is usually associated with drinking raw unpasteurized milk.  E. coli is another bacterium found in calves that can infect humans and can lead to bloody diarrhea, kidney failure and even death in children less than 5 years of age.  It is believed 20% of herds are positive for E. coli and 75% of the calves taken to Minnesota county fairs in 2006 were positive for E. coli.  Almost all dairy farms have the protozoan cryptosporidium parvum that can lead to diarrhea in children. 

So just like with COVID-19, hand washing or wearing gloves is critical to prevent transmission of these diseases from calves to humans.