The short answer is that this diet is perfectly safe.
Many people world wide don’t drink milk, either because it is not available in their part of the world, or because it makes them sick. Is milk safe? That in itself is a loaded question, which I will not answer here! Certainly not drinking milk is safe.
Gluten itself is not essential to human health in any way shape or form. Not that it is bad either, unless you are allergic to it or you are a celiac. By cutting out gluten, you are cutting out wheat. What does this cut out of your diet? More unhealthy food than healthy food, in most cases!
Most people worry that by cutting out milk, they will reduce their calcium intake, and suffer from osteoporosis. Firstly, there are many other foods that contain calcium. Secondly, the highest rate of osteoporosis in the world coincides with areas that have the highest milk consumption.
As for cutting out wheat, it is inconvenient. But nothing more than that.
The refined wheat that most people eat in cakes, cookies and breads has little nutritional value and is high in simple starches, which is not healthy.
In Southeast Asia, the diet is naturally both gluten-free and milk-free. They use rice and soy instead, among other foods.
By cutting out milk and wheat from your diet, and looking for healthy food to eat instead, your diet will be safer and better.