I just watched a video that discussed this movement. It is closely aligned with the fat acceptance movement.
I totally support body acceptance. People should not feel shame about their appearance. But, the Health at Any Size movement is most definitely spreading misinformation about the health effects of obesity on ones health. Like many movements these days, online communities develop and people start talking in echo chambers.
Yes, there is a huge genetic component to who tends to gain weight and who doesn't. But, the Western diet of constant calorie intake in the form of high carbohydrate foods is hurting people's health. And the uptake in obesity is contributing to many chronic modern diseases.
Healthcare practitioners should be exhorting people to improve their diets. So many of our current health problems result from people just packing away too many donuts and soda pops. The food industry is a big problem. The school system also gets kids started on junkie school breakfasts and lunches Laden with sugar and empty calories. This is a public health crisis.