The Constitution protects economic liberty,  but only against regulations that lack a rational foundation in a legitimate governmental interest. 

Two recent cases from the U.S. Court of Appeals for the Fifth Circuit show how slippery this principle can be in practice. The underlying principle is alive and well, but "rationality" is a fairly easy burden for a regulator to satisfy. 

In one, a Louisiana ban on the making of funeral caskets by Catholic monks was struck down (in no small part, because the ban served to benefit the funeral home directors who controlled the relevant agency). 

In the other, a Texas ban on telemedicine by veterinarians was affirmed, by a 2-1 vote, on the rational basis that pets cannot talk while humans can. (The dissent was swayed by the argument that babies cannot talk either, but we allow pediatricians to treat them by telemedicine).