As has been said numerous times above; tap water in most countries does not contain harmful bacteria. It is usually treated to stop that from happening, and therein lies the problem. The treatment that kills the bacteria plus anything it picks up on its way through miles of possibly ancient pipes, may well not be a good thing to have sandwiched between a lens and your eyeball. It *probably *won’t do any harm, but why take the risk?
Tap water is dangerous in exactly the same fashion as crossing the street is dangerous.
The overwhelming majority of human being who partake suffer absolutely no ill effects or adverse events their entire lives. Sometimes, something bad happens. Sometimes out of carelessness, sometimes out of sheer bad luck.
Life is risk.
Dihyrdrogen Monoxide has never been safe.
This is what my optometrist told me. Eyes are delicate. There are plenty of things you can drink without issue that might cause problems if introduced to the eye.
The chicken thing (as described by the OP) is dumb (to be clear: I’m not saying the OP is dumb). If tap water is safe to drink, it’s safe to wash chicken with. The chicken cross-contaminating the sink and nearby things is a reasonable thing to prevent, though.
Eyes are delicate, sensitive body parts that will react badly to having things put in them that are safe to eat. This is really easy to demonstrate - if you take a nice fried egg with salt and pepper and eat it, you’ll be fine, but rub it in your eye and it will hurt. The reason not to wash contacts with tapwater is not that tapwater is extremely dangerous, but that the eye is extremely sensitive and sterilized saline solution is much better for it than tapwater.
I don’t know of any reputable source that says not to wash chicken because the tap water will contaminate the chicken. The advice I’ve always seen is not to wash the chicken because splashing cold water will come off of the surface of the chicken and spread any possible contaminants in the chicken to the sink or nearby dishes, which can then make their way to your mouth without being cooked. Raw chicken is not considered safe to eat, but cooking it kills any of the likely dangers - but you don’t cook clean dishes or vegetables that maybe touch the sink or your upper arms where washing might splash water.
There’s no reason not to wash a regular wound with tap water, though some really severe injuries may need special treatment.