As many people have noted, it doesn't matter if fat people are unhealthy. Unhealthy fat people deserve dignity and equal access to public spaces, medical care, clothing that fits, etc.
And it doesn't matter if fat people are unhealthy because of they way they eat. No matter what they eat, or how much they eat.
But I feel like in the struggle to make people understand this, we have fallen into a trap of labelling foods as either unhealthy or healthy. While the goal is to say it's OK to eat "unhealthy" foods, this is still diet culture talking.
When you label foods as good or bad (healthy or unhealthy), you tend to think of your eating habits, and yourself, as good or bad depending on what you ate. The answer isn't to say that "unhealthy" isn't bad. It's to remove all judgement labels from food (other than saying things like "this tastes good and I like it").
If you're saying to yourself, oh, eating ice cream for dinner would be unhealthy, instead you need to ask yourself:
Do I need to fuel my body?
What's available for me to eat right now?
What do I have the energy/spoons to prepare?
Will this food make me feel good emotionally?
How will this food make my body feel?
If the food you want fuels you, is available to you, you can prepare it, and it makes you feel good, then it is the right choice for you. There is not a healthier option in that moment. Could you eat a salad? Maybe, but maybe that won't satisfy you, either physically or emotionally. And if it doesn't satisfy you, then it isn't the healthiest choice for you, in this moment.
Black and white thinking about the value of foods can lead to eating disorders. Talking about food this way will especially screw up kids, folks who are limited in what/how they can eat (autistic folks, diabetics, folks with IBS, etc), and people who are struggling with eating disorders already.
Remember also that all food has nutritional value. Fats, sugars, and salt all fill nutritional needs. And we all need calories to function. Don't get hung up on whether something is "nutritious" enough.