You didn't read the article you cited, or if you did, you didn't understand it.
The least civic minded and militarily engaged states are almost entirely BLUE.
If you look at the methodology used, under military engagement there's this:
Active-Duty Military Personnel per 100,000 Civilian Adults: Double Weight (~7.14 Points)
California gets more points because it being roughly 75% of the US West coast has considerable military bases within the state. Yet, it ranked 48th for the number of veterans per 100,000 population. That is to say, the vast majority of military personnel stationed in California are not from California, and don't stay there when they get out. Put another way, California is not military friendly, but rather has little choice but to tolerate its presence.
Hawaii is yet another example of this with a very high number of military personnel stationed there who are not Hawaiians.
The same goes for the civics scores. You'll note that their methodology favors the Left in how it determines this score.
As an example of that, the ultra-Left SF Bay area up through the 70's was home to numerous military installations including:
Naval Station Treasure Island
Mare Island Naval Shipyard
NAS Alameda
NAS Moffitt Field
MWS Concord
Naval Shipyard Hunter's Point
the Presidio
Numerous coast defense forts
Port Chicago
etc.
Virtually all of that has left the Bay Area. Why? Because it was politically unfriendly to the military.
So, it's the RED states, particularly the most Left leaning, like California and New York that are the
least patriotic. North Dakota, a Blue state is an outlier due to its small population and large percentage of native Americans within the state.