Is butter required to caramelize onions?
Onion can be caramelized without butter. Or any other type of oil. However, unless you are actively avoiding using fat, there really is no reason not to.

The main benefit of using oil when caramelizing onion is the fact that oil can reach a higher temperature than water. To caramelize onion you need to reach about 230F. Water boils at 212F and will not go higher than that. So to caramelize without oil, you would first need to draw out the water and "dehydrate" the onion a bit before they reach temperatures that can caramelize the onion. Note: Never put water into the pan if you wish to caramelize onion.

The reason you very commonly see butter used is because it can reach temperatures above 230F and it's flavor profile works really well with the savory sweet flavor of caramelized onions.