I am very aware that Rhode Island has significant numbers of people in poverty, especially around Providence. I don't think it's anywhere close to DC's situation, though I could be wrong, of course.
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.