I am very much dedicated to hygiene. (I wash my hands every time I have touched any of our animals [chickens, cats, or dogs], door knobs, or faucets, before I touch my face or handle food. I also wash my hands at numerous other occasions, and we disinfect door knobs, faucets, and computer keyboards on a regular basis..)
However, I must say that when I grew up, in Germany, during WWII and the years following, hygiene wasn't up to today's standards, and our chickens were pets. They were actually my first pets (as there wasn't enough food to feed a cat), and they got handled a lot.
I never got sick as a result from handling our chickens, who liked to be picked up and carried. (I had them trained to spread their "elbows" on my command "duck duck!" for easier pick-up.) After the end of a day's work, my grandmother would rest on a chair, and the chickens would line up to get onto my grandmother's lap to get their fluffy behinds massaged, which, I must admit, were occasionally covered with lice. (I don't think that there was any suitable insecticide available at the time. Several years after the war, DDT became available. I don't know whether it was used on our chickens and they survived it. I only know that friends treated a flea-covered cat, they had recently adopted, with DDT, and the poor thing died a horrible death.)
None of my family members, who all handled chickens and none of whom adhered to hygiene rules too much, ever came down with any illness that could be blamed on handling chickens.
I have, meanwhile, read several books on germs and hygiene, and found that washing my hands about 50x a day is still not enough to avoid all dangers from household germs, but greatly reduces these dangers. I am an advocate for adhering to hygiene rules (with or without handling chickens), but I would consider it an overkill to refrain from treating chickens as pets because of fear of contracting illnesses.
We have obtained baby chicks, last spring, which have just started laying eggs. We consider these chickens pets, and they love to come onto our laps and also to sit on our shoulders. (Unfortunately, they, so far, don't like to be picked up. I also have not yet accomplished to teach them "duck duck!".) I use extra garden/chicken-yard shoes when I enter any of the chickens' residences. I check my clothes for "accidents" after close contact with the chickens, and I wash my hair when our chickens got into it. Thorough hand-washing is a no-brainer anyway.
The world is filled with pathogens. Avoiding animals is not the answer to stay safe. Hygiene is. (The danger to contract a serious illness from a human is much higher than to contract any illness from an animal.) Yet no matter what one does, germs cannot and should not ever be avoided 100%. There is always a remaining risk.
There remains the danger of bird flu, which we take very seriously. (I have suffered 10 pneumonias and numerous other serious respiratory infections throughout life, most of them during times when we had no chickens. Any new respiratory infection, of whatever source, could be my last one.) Bird flu is a danger to all bird keepers, no matter whether or not they treat their chickens (and other birds) as pets. Luckily, there is a good chance to hear about bird flu from the media before a pandemic will hit one's own chickens. So bird-owners can take precautions (best before any bird flu erupts anywhere on our globe).
We have automatized feeding and watering, installing devices from outside. In case bird flu hit our area, we could care for our chickens without entering their predator-safe enclosures. (They have a winter residence, near the house, with a small run, and a summer residence, farther away from the house, which a huge run.) Mind you, the manure would pile up, but this would probably be the lesser of two evils. If bad came to worse, we could enter with rubber boots, gas masks, and hazmat suits (which we own) and go through a complicated disinfection procedure, after leaving the enclosure.
If you are afraid of contracting illness from your chickens (which, definitely, is a possibility), make sure to take the proper precautions. But don't overdo it. Always keep in mind: Veterinarians are constantly exposed to zoonotic pathogens, and they haven't become extinct yet, even though most of them do not practice hygiene as much as I do. :-)