There are lots of reasons to drop dairy and gluten. Personally, I had to do it due to a common genetic mutation (MTHFR); some people have allergies, and others have food sensitivities, noting a correlation between types of food and symptoms, and acting on it.
I made the dairy-free gluten-free switch about a year ago, and within just a few weeks, I noticed all kinds of improvements. My heartburn vanished. My foggy-headedness lifted — it felt like cotton balls were removed from my brain. My stomach stopped gurgling all of the time. I had more energy. My allergies seemed to go away and never come back.
I have to admit, at first I was like, WTF am I going to eat?! It was so daunting. But it's not as bad as I thought it would be. If I had known the following advice a year ago, it would have made going gluten- and dairy-free even easier.
Learn to love quinoa. I don't know anyone who dislikes it, actually. It's the same texture and non-taste as rice, but it's way more nutritious. It's also used as a replacement in many pre-made gluten-free foods, like pastas. (Look in the "healthy" section of your grocery store.) I'm not particularly picky about pasta, but I can't tell the difference. Be very careful to not overcook quinoa dishes, though — they'll get weird fast.
Nuts make great ice cream. My goodness, this was such a delightful surprise. Turns out I love frozen cashew treats even more than I love ice cream. I had no idea it could be so good! And it's comparable to Ben & Jerry's price-wise, so you don't have to find any extra room in your budget to make the switch.
Nuts also make great cheese! So. Good. You probably don't believe me and just think I'm coping with losing cheese — and you might not be totally wrong — but nut cheese is seriously tasty. (It doesn't melt, though. And all the ones that do taste like dookie, if you ask me. But hell, there's vegan shrimp now, so something better has got to be on the way... I hope!)
Bechamel sauce like whoa. Generously coat a pan heated to medium with olive oil, add few tablespoons flour substitute (I like garbanzo), stir until mixed well, add in unsweetened almond milk, stir, and repeat until it's almost as thick as you'd like it. (It'll keep thickening — keep the almond milk on hand.) Add in fresh herbs and garlic. BOOM. Delicious.
Eat out when you can. Luckily, I live in Portland, Oregon, where there's almost always vegan (no dairy) or gluten-free menu labeling and options. When there's not, I look for for: rice, corn tortillas, meat (I do still eat meat), or salads with safe dressings.
It's really not as bad as I thought it would be! And I'm always open to more tips, so please share any that made switching to a gluten-free, dairy-free diet easier for you.