Why are red states' workforces more dominated by public workers than blue states?

Here's a chart of state and local public employees as a percentage of the population in each state.

It's not surprising that Washington, DC, as the seat of the federal government, has a lower percentage than any of the 50 states, since we're not counting federal employees.

What is surprising is that the states with the largest such percentages are overwhelmingly Republican-leaning. The 10 states whose workforces are most dominated by state/local public employees have 8 solidly Republican states, with only 1 swing state (New Mexico) and 1 Democratic state (New York, whose percentage is still far from the highest).

The 10 states with the proportionately smallest state/local public workforces are a mixed bag of red, blue, and purple states, including the deep-blue Massachusetts.

Catherine Rampell, the author of that New York Times blog post, crunches the numbers and finds that, indeed, "the more dominated a state is by [state/local] public-sector workers, the less likely that state was to vote for the Democratic presidential candidate."

The state with the highest percentage is Wyoming. You might think this is an anomaly because it has the smallest population; therefore, basic services and infrastructure require a higher percentage of its workers. Similarly, a commenter on the Times post says:

The results are largely explained by geography and demographics. With respect to geography, for example, most state and local employees are employed in the educational sector. States that are not densely populated, such as Wyoming, tend to have a lower teacher-to-student ratio (Wyoming has an average ratio of 1 teacher to 13.1 students and the average national ratio is about 1 to 24 as reported here on Economix). Also, low population states such as Wyoming and Alaska require relatively higher ratio of employee to general population to deal with basic governmental functions (each state has the same number of governors, etc)[.] Econom[ies] of scale play[] a role here.

That wouldn't seem to gibe with Rhode Island, which has one of the smallest populations and the 6th-lowest percentage of state/local public workers. But that commenter has an explanation: the states with the highest percentages have a large area, so they need lots of government for things like highway maintenance.

Rampell observes:

[I]t is not such a big contradiction for states to be hostile to candidates perceived to be expanding the size of the federal government, and to still employ lots of workers at the state and local levels.

Maybe we should stop equating "red states" with opposition to "government." They merely tend to be against the federal government having a major role in their lives. And isn't that natural? They have relatively little need for it -- they already enjoy so much help from state and local government.