It is probably useful to eliminate, but might not practical. What will your child drink during snack time if not milk the school provides? Can you send something instead that you feel is a better alternative? If so, send it. What do you allow him to drink at home?

I think your instinct that finds it hard to restrict milk when you have already restricted cookies is right on. You must find a balance for school aged children and give up the notion that they will only eat paleo 100% of the time. If diet problems are so detrimental to his well-being then you must find a way to provide all of his food/drink items while at school and make sure the teacher adheres to your standards. Not very practical, but necessary if his health is threatened. However, if his eczema has improved already with the elimination of grains, then just give his body more time to allow for further improvement. Or eliminate dairy at home and allow him the one milk a day at school. Keep in mind if his eczema improves, it could be hard to determine if it was due to more time healing from the grain elimination or decreasing the dairy.

In the end, us parents who cannot stay home with their children or home-school their children must find a practical balance of nutritional health for their kids and allow some variance as perfect nutrition is not attainable in a public environment.

As a person who is dairy allergic, from childhood, and my mother did not eliminate it, I can say from my own health problems in adulthood, that I'd eliminate it completely. I actually have eliminated it in my oldest (who is allergic) and my younger 2 (who are not allergic) get dairy very rarely. Coconut milk yogurt and coconut milk smoothies are a great sub. As is almond milk.

The answer is "it depends."

It depends on what type of food sensitivity, if any, is involved.

Milk allergy is caused by IgE antibodies to one or more protein components of the milk. Symptoms can include cough, wheezing, nausea, headache, hives and eczema. This type of hypersensitivity can be tested by either skin prick or blood test (RAST), so a dairy elimination diet may not be necessary for testing purposes. (Reference)

Your son may have a delayed-type hypersensitivity to dairy (mediated by T-lymphocytes, not IgE). There are a few delayed skin tests for antigens such as tetanus, yeast, tuberculosis and poison ivy (Ref.), but I don't know if a delayed cow milk skin test is available. Usually the best way to test for delayed food sensitivities is to completely eliminate the suspected food (dairy) from the diet for a few weeks. If the symptom (eczema) improves, then re-challenge with dairy to see if the rash worsens. Partial elimination of dairy may work for this test, but complete elimination would probably work better. (Ref.)

Regarding treatment, delayed hypersensitivities are dose-dependent, while IgE-mediated hypersensitivities are not. This means that only complete elimination of dairy will be effective if your son has IgE-mediated milk allergy, but a partial dairy elimination may be effective for a delayed cow milk sensitivity.

If it's a diet irritant and you can find a way for him to avoid it all together let it go. It can lead to a host of other problems down the line. If you are going to have him drink milk regardless make sure it's from a grass-fed, super clean source. That's not going to be what they're serving up at the school. So regardless, I'd say morning milk at school should be off limits.

For me, dairy right now isn't sitting right. While I wasn't eating paleo, dairy sat fine with me, but now that the grains and sugars are fully out, my gut presently isn't liking milk by itself. I do still eat yogurt that's been fermented for twenty four hours. That works great for me. I can also do Raw milk if I feel like tracking it down and affording it. Play with those options.