Until recently Elmer's Glue was made by Borden Chemical, which was once primarily in the dairy product business. This has led some people to wonder if Elmer's Glue is made from dairy products. Apparently it is not.

This is a page where Elmer's Products addresses facts about how Elmer's Glue is made.

They say

Elmer's Glues are chemical based. They are made or formulated from chemicals which are synthesized (created by Man).

That tells you nothing. Below is where the information about where it comes from, is contained:

These chemicals were originally obtained or manufactured from petroleum, natural gas and other raw materials found in Nature. The exact formula and specific ingredients used in making Elmer's products are considered proprietary information, therefore, we cannot share those with you.

Everything, of course, can be traced back to "raw materials found in nature." There is nothing else extant, except perhaps supernatural things found in an alternate reality. The term "other raw materials found in Nature" does not rule out found animal products such as trapped or hunted animals, or animal products obtained via animal husbandry, products made from farmed animal. But to the best of my knowledge modern glues are not made from such animal materials, to any substantial degree. Yes, they might be filtered thru bone char, or packaged on assembly lines that have been lubricated with petroleum grease with some animal-derived fatty acids added to them. But that is possible with just about ANYTHING you don't make yourself from scratch.

They also say

Elmer's does not use animals or animal parts to make glue. Our products are made from synthetic materials and are not derived from processing horses, cows or any other animals.

They go on to say

I have a milk allergy, are your products safe for me to use?
Our products are derived from synthetic materials, not any type of animal or milk protein. Of course, if you experience any kind of allergic reaction, be sure to check with your doctor regardless of the type of product you are using.

While they insiste that there is nothing derived from "processing horses, cows, or any other animals" in their products, their MSDS data sheet for Probond Regular Epoxy Resin, states that the product contains fatty acids. Fatty acids may be made from animal fats (such as fat obtained from slaughtered cattle or pigs) or vegetable fats. Xommercial sources of fatty acids aret typically 60 percent animal based and 40 percent fat based.