There are several red states with no state income tax. Texas and Florida for example, so I assume you're talking about property taxes and taxes on items like gas or food?
Tax is tax, does not matter whether it is income tax, sales tax, car registration fees, tolls, unemployment insurance, estate tax, etc. If it is mandatory, and it eventually goes into government coffers, it all falls into the “government expense” bucket for an individual.
I like to think of property tax as a wealth tax for the middle class. My understanding is that the per capita taxes of those states aren't really much different from others, but they're structured more regressively.
First, there is no middle, it would be more useful to describe socioeconomic classes of people by decile, or even quintile.
But the top 10% surely owns more real estate than the bottom 90%, so low property tax is very regressive since it allows them to hoard real estate, while the rest of the population pays to secure it via funding the police/legal system.
Second, the lower socioeconomic classes are going to spend all of their money on rent, and goods and services, like consumables and healthcare and food and tolls. So sales tax and usage based taxes for things necessary to live are the most regressive.
Third, property tax can be broken down into land value tax and building value tax. The former being low is a problem since it incentivizes hoarding land at less than maximum economic usage, ultimately reducing supply of housing, ultimately increasing rents on the lowest socioeconomic classes amongst other phenomena like food desserts.
So if the goal is progressive taxation, then a very high land value tax, and no building value tax would be the way to go.
Funny you say that, because not only do 'red' states have higher crime rates than 'blue' states[0], but 'red' cities within those red states, like Jacksonville or Oklahoma City, also have higher crime rates.[1]