The main reason I think Skins fans hate the Cowboys is because their fans are so obnoxious. The type of people who grow up in DC and root for the Cowboys are generally the absolute bottom tier of the human pyramid... they're generally loudmouthed, borderline criminals, who root for Dallas not because they actually like the team, but root for Dallas to compensate for the attention their parents didn't give them. They are all attention whores of the highest order, and growing up in DC and rooting for the Cowboys is akin to growing up in America and rooting for the Nazis during World War II. It's like the part of their brain that control higher functions just doesn't work, so they just hang out at gas stations in Romo jerseys opening their mouths only to spout BS and drool.
Seeing a person in a Cowboys jersey in DC tells me absolutely everything I need to know about that person. I can only take solace in knowing that they probably won't accomplish much in their lives because in all the years I've lived in DC, I've not met a DC-native that was a Cowboy fan that wound up amounting to much of anything.
Cowboy fans who grew up around Texas I have no problem with. If I grew up in Dallas, I'd probably be a Cowboy fan as well. I'm a home team guy.