As a high carb low fat vegan, I avoid fat and salt. I explain why in this selection from my e-book, Eat Like Me: High Carb Low Fat for Beginners.
We do need trace amounts of fat to be healthy. Even if you completely avoid overt fats like oil or nuts, you will still consume plenty of fat in your diet. Fruit, veggies, and starches contain small amounts of fat. All these small amounts add up at the end of the day.
Ditch the oil.
Cooking with oil is unnecessary and a waste of calories. If you want to roast veggies, line your pans with parchment paper. This allows you to skip oil entirely because the veggies won’t stick to the pan. You can also sauté veggies without oil: heat a sauté pan over medium-high heat. Once the pan is hot, add your veggies. Stir them often with a rubber spatula (if using a coated nonstick pan, otherwise wooden tools are fine). If they start to stick, add a splash of water (or veggie broth), cover the pan and turn down the heat a bit. The steam from the water will loosen them.
Cut out the salt.
You never need to add extra salt to your food because veggies naturally contain trace amounts of salt. Our palates are so messed up from eating overly salted processed food and meals from restaurants. It will take time for your palate to readjust to salt-free cooking, but once you go salt-free at home, you won’t even miss it. Try to keep your salt intake to a minimum but don’t obsess over it. Choose low or no sodium options for tomato sauces, tortillas, or packaged snacks when cooking at home.