One explanation for Robert Reich's question is that workers in Red States vote on cultural and value issues. That may be part of the reason, but the other reason is economic. The red states are able to attract businesses and jobs to their states by being "business friendly". When jobs are scarce workers vote in their economic interest.
Reich does not consider another question that is related to the issue that he raised. That is, why might business leaders prefer a less than full-employment economy? One might expect that more growth and output is in their interest. That may not be true. For example, corporate profits in the US have been at an all time high under conditions of high unemployment. To some extent, the high profits are the result of stagnant growth in wages. It is easier to control wage growth when we do not have full-employment. At a deeper level, it also gives business leaders more power in relation to government officials. Politicians understand the importance of jobs. In every state, and in every nation, they are in competition with each other to attract jobs to their area of responsibility. That is only possible when jobs are a scarce commodity. Full employment would be very bad for business. One of the benefits of globalization is that it is easier for businesses to move jobs from places with high levels of employment, and high wages, to locations with higher unemployment and lower wages. They can also do so without worrying about the loss of consumer demand in areas that they vacate. They can replace the demand in mature markets with demand in more rapidly growing markets.