Not necessarily.
Whey protein is about as processed as a food can be, and few people view it as an inherently unhealthy food.
The fact is, processing takes many forms; we are even “processing” food as we cook and chew it. When people talk about “bad” processed foods, they’re generally referring to foods that are highly processed, largely devoid of fiber and micronutrients, and extremely palatable. Such foods can absolutely be incorporated into a healthy diet, but many people find that they tend to exceed their daily energy target or fall short of their fiber and micronutrient targets when their diet becomes too reliant upon highly palatable, ultra-processed foods.
So, these foods are not inherently bad and need not be avoided entirely, but healthy diets generally tend to include plenty of minimally processed, micronutrient-dense foods in conjunction with some more processed foods.