Obviously there are aspects of a BosWash corridor culture but DC is very much ''New South'' in my opinion. Grew rapidly after WWII, lots of new suburbia, and the like which is very UN-Northeastern. No Italian or ethnic Catholic presence. PG County doesn't seem very ''Northeastern'' (far more like suburban Atlanta than SE Queens). It's at least as much like Atlanta as Philadelphia.
If Atlanta was the national capital it wouldn't be all that ''culturally Southern'' either.
It's more than 25% African American, has virtually no white working class and is filled with highly educated people who work for the federal government. Being (sort of) "in the Northeast" has little to do with the liberalism of the area.
Another factor that aligns the DC metro more closely with the Northeast, in addition to the obvious infrastructure ties to the Acela Corridor, is the absence of white Evangelical culture. It’s receding even on the Virginia side, but is almost completely absent on the Maryland side until you get out to Anne Arundel County. Maryland’s white Evangelical population is so proportionately low that the percentage resembles New England states more closely than any of the surrounding states.
You can’t really call a place Southern if Evangelical whites struggle to crack double digits in terms of percentage of the population.
I think a lot of that can be explained by the Federal Government thing (a national capitol in Atlanta, as King of Kensington pointed out above, would probably look a lot like DC demographically) and by the fact that much of Maryland is historically Catholic (though I'm not certain precisely the extent of this in many of the DC suburbs so it probably shouldn't be overstated). Southern Louisiana, as I'm sure you know, is predominantly Catholic and is of course Southern despite its distinctive origins.
New Orleans and Baltimore are actually pretty good comparisons as they were both the early large industrial Southern cities which got a lot of immigration.