I'm not a vegan or a vegetarian. I don't eat a gluten free diet. I drink milk and I eat eggs. It seems there is no end to diet fads, but I can eat a healthy diet without falling for the fads.
Vegan and vegetarian
Sorry, but a quick look at my teeth tells me that people are meant to eat meat. Either God gave us meat eating teeth so we can eat meat, or millions of years of evolution have made us meat eaters, or both. (Actually I believe it is both) Now, I understand some people don't like to eat meat, that is fine, it is their choice. However eating meat provides a lot of nutritional benefits. http://authoritynutrition.com/7-evidence-based-health-reasons-to-eat-meat/
Gluten free diet
It is true that for some people, like the 1% of people with celiac disease, gluten is a problem, but for the other 99% of us, eating gluten is not a problem. In fact there are a lot of foods that provide a lot of great nutritional value that have gluten. Going gluten free denies us the opportunity to eat these good foods. http://www.webmd.com/diet/healthy-kitchen-11/truth-about-gluten
Milk
I hear the argument that it isn't natural to drink milk into adult life. Wrong. I am of northern European descent. Well, mostly northern, with a bit of Czech. There are thousands of years of people living with cows, and drinking their milk and eating dairy products. We have a symbiotic relationship with domesticated animals. Our domestic animals exist because we bred them, and in turn they have given us food and protected us from disease, like small pox. My ancestry has a long history of eating dairy. So even though most of the world can't drink milk as adults, my ancestors genetics have evolved to make milk drinking good for me. http://www.nature.com/news/archaeology-the-milk-revolution-1.13471