I find the word "fast" freaks people out, but if I simply say that I only eat when I'm actually hungry, people accept that because that sounds healthy and normal, while the idea of fasting makes people think of eating disorders or religious practices.
Also, I explain (only if asked!) that I have celiac disease (true) and so generally avoid grains, plus I prefer to get my carbs from more nutrient-dense foods like vegetables, which people also happily accept since vegetables are good for you. People are also very much okay with the idea that I don't generally eat sugar (again, CW says this is good too), and that I don't eat processed foods. They also totally get the idea of eating local, seasonal foods.
The fat thing is weirder for people, but it probably helps that I don't do full-on LCHF, although the amount of fat in my diet would still give a CW nutritionist nightmares. But again, if I say that I prefer natural fats over things like processed vegetable oils, people get it. More people are starting to understand the whole dietary cholesterol myth because that's been talked about in the mainstream media enough that it's sinking in, at least with people I know.
I think a lot of the acceptance I get of my diet has to do with how I frame it, rather than the actual food practices themselves. Also, I don't preach or push my choices, and that makes a huge difference too.