The argument that citizens can't possibly have a right to food, shelter, clothing or health care because it would require some people to be farmers, builders, clothiers, and doctors only makes sense for anarchists. As you pointed out even a minimal government that sets, enforces, and judges the law would require some people to perform the necessary jobs.
It's not really about negative or positive rights but about what products and services are best provided by government and which by the private sector.
In most cases the services and products are provided by the private sector with varying degrees of government oversight, e.g. dams requiring much more than soft drinks.
Further: No discussion of "rights" is complete without a parallel discussion about "obligations." A lot of the "talk" about what is "owed" to "poor / underprivileged / historically disadvantaged" people would evaporate if we insisted that the corresponding "duties" of those same people receiving govt. largesse also be discussed.
Most of the people arguing about the "right" to free health care, free education, etc. couldn't explain, e.g., the difference between a "right" and an "entitlement" if their lives depended on it!
In most cases the services and products are provided by the private sector with varying degrees of government oversight, e.g. dams requiring much more than soft drinks.
That might seem to be the case (that dams deserve more govt. oversight than soft drinks), but one could argue that (sugary) soft drinks (resulting in obesity / diabetes) have actually resulted in the loss of more man-years of life in the U.S. than failed dams.
(I'm funnin' yuh there!)
Regards,