A big money save is a chest freezer. When an item goes on sale, buy it in bulk and keep it in the freezer.
I buy half a cow of beef at a time from a local rancher. It tastes much better than grocery store beef, and it happens to be cheaper.
But you can put butter, cheese, veggies, and all kinds of other goods in a chest freezer, too.
I think this is an issue that both sides can agree on. I plant a garden every year and can vegetables and some fruit. Lots of work, but I know my food is fresh and packed properly.
I don't like processed foods and it is cheaper to buy fresh chicken and make it last, like the poster above talked about. Buying that frozen chicken that you heat up is expensive and probably tastes like crap.
A person just needs to be a bit creative, look for sales, use coupons and freeze items that you get on sale. I think people would be healthier and their budgets would stretch if they were willing to bake from scratch instead of going for convenience.