The reason you shouldn't touch a caterpillar with your bare hands is because many caterpillars have venomous spines or even hairs which can break off into your skin and cause intense itching, pain, swelling and rashes.
Some bright or fuzzy caterpillars also warm their predators and irritants (setae) which can cause reactions even without coming into direct contact with it.
The best thing to do, is to avoid touching any caterpillar unless you're sure that it's harmless, like some Swallowtail caterpillars or Monarch caterpillars.
Although Monarch caterpillars are also toxic when eaten and many fuzzy or brightly colored caterpillars are also dangerous.
If you do want to touch or pick up a caterpillar you should wear gloves to avoid any issues and avoid the caterpillar from coming into contact with your skin.
Hairy or fuzzy caterpillars like the Puss Caterpillars, lo Moth caterpillars have hollow spines, which are connected to venom glands which inject toxins upon contact and causes symptoms that are similar to those of bee stings.
And even non venomous caterpillars have tiny hairs or setae, which can detach and get stuck in your skin and trigger allergic reactions or even rashes.
Caterpillars with bright colors like red, green or black often signify that the caterpillar is toxic, so touching these caterpillars with bare hands is risky as they are designed to deter any predators.
If you do touch a caterpillar with your bare hands, remain calm as most reactions are temporary discomfort and not serious harm to you.
You can use some tape to gently pull off any embedded hairs or spines and gently wash the area using some soap and water and then allow it to air dry and avoid rubbing the area.
You can also apply some baking soda paste or hydrocortisone cream for the itching, and even antihistamine cream can help.
If you notice any signs of infection, or severe allergic reaction you should seek medical attention.
But most often at home treatments will be good enough.