I don’t think this is true. Rhode Island has tremendous wealth disparity.
https://www.providencejournal.com/news/20180210/studies-inco...
And just to be clear, right behind DC and Rhode Island we have Alabama (OK, maybe poverty). Then just a few % above them New Hampshire, Kansas, Alaska, Pennsylvania.
These are all quite different from each other on various socio-economic and geographical axes.
And of course the states with the most successful vaccination campaigns in the US (with ~98% of vaccine supply used) are West Virginia, North Dakota, and New Mexico. Which are also quite different from each other in various socio-economic ways.
So it's hard to blame the socio-economic angle for the state-by-state disparities here, though I would be quite willing to look at data showing otherwise.