Unfortunately, this isn't true. In many non-privileged areas you may have supermarkets like c-town, associated, fine-fare, or other non-boutique supermarkets that mostly stock mainstream products from mainstream food producers, as such they usually have very limited selections of organic and non-GMO foods, if any. So unless rules like these are passed, those groups are reliant on companies changing their behaviors based on market trends (such as rice krispy treats removing high fructose corn syrup from their boxed product). Worse, even in those cases most large food producers tend to roll out the "healthier" products specifically to the privileged areas, leaving the non-privileged with "worse" product.

I think issue of limited (and bad) food options has less to do with government regulations and more to do with the economics of those areas.

Apparently you've never been poor or lived in a food desert.

Poor people can't buy Organic non-GMO things; they're not affordable. If we ban this, they stop consuming it. Later in life we aren't picking up the tab for their health issues.

It just makes good economic sense and it's moral, too.

I think the "known to the state of california to cause cancer" warnings are on so many things that they are effectively meaningless. So that's probably an example of a required warning that has little effect.