Here is some info from the Elmer company on the composition of the glue.
http://www.prnewswire.com/news-relea...200905731.html
This information is from another source - Reference.com
"Some glues are made from the connective tissue of animals, particularly horses. However, Elmer's Glues are only made from man-made ingredients and are safe for use by people with milk allergies.
Elmer's School Glue, the white type used by children for arts and crafts projects, can be removed from surfaces by applying warm water or a cloth soaked in warm water. However, this method does not work for removing glue from clothing. To get the glue out of fabric, soak the material in room temperature water for 24 hours or more to soften the glue, then it can be washed as normal and air-dried."
so it looks like if glue is stubborn, a soaking might help. I just washed another completed glue basted quilt and it is very soft, so maybe the thin line of glue I use did wash out.
The question about migrating to the batting doesn't seem to be an issue since it is apparently made from natural plant materials.
I wonder if the other brands are the same. I've used Target brand with good results. I don't know who makes it and what the formula is.