I am sorry to hear your family are being butt-heads about eating healthy. Since they are adults, then they should be given some responsibility for what they eat. I would cook the good stuff (homegrown) and let then know that is what I am making for supper. They can eat it or not. If they don't want to eat it, then they can get their own supper or go hungry. If they are like a lot of my family, they will eventually get tired of going hungry or cooking for themselves. Who knows, maybe one will find they like to cook and you will get a kitchen helper out of this.
My hubby is the same way about stuff, not really any rhyme or reason for some of his boycotts. For instance, I like to garden and one year I was looking through a seed catalog and they had a mushroom box - for growing button mushrooms. He said "absolutely not!". I wasn't really set on getting it, so I didn't; but some day soon I will grow my own mushrooms and home can or dehydrate the extras. I use a lot of mushrooms in my cooking. I am not sure how he will react to me making yogurt... we will see soon. lol! He knows I am not happy with the stuff I can get from the store here.