Pure oats are 100% gluten free. If you find something like oatmeal or oatmeal cookies with Gluten, they added something else. So if oat milk is really from oats, there shouldn't be any gluten in it - as suggested by someone above.
I do agree with you that gluten for most is no issue. I stay away from Super Gluten - the genetically modified crap that makes wonder bread taste like air and salt. But pure milled grains - no problem.
Yes, technically, pure, uncontaminated oats are gluten-free. However, there's a substantial risk of cross-contact due to how oats are ...