If taxpayers are financing people's grocery bills on the theory that they and their children will be unhealthy and malnourished if we do not, then of course we have a right - and a duty - to make sure that our money is not spent on unhealthy junk.
If I could only ban one thing, it would be sugar-free soft drinks. It would be far more healthy for welfare kids to drink tap water, flouridated or not, than to be given "free" Diet Coke and the like.
Spend SNAP money on juice, if anything. It's almost as high in sugar as cola, but at least there are some vitamins, and it is not addictive as are the sugar substitutes, and caffeine in diet soft drinks.