Literally an article from 12 years ago. That's one instance in over 1500 sporting events.

I’m a Philly fan and really the Eagles fanbase is the most like the stereotypical obnoxious Philly fan moniker. That being said you might be made fun of, harassed, etc, but you won’t be physically attacked at all unless you provoke it. Nobody vomits on random children (purposely), nobody throws batteries (anymore) and nobody boos Santa (unless he’s drunk and embarrassing himself). Nobody will randomly punch you and if they would I think most eagles fans nearby would actually have your back because nobody in Philly likes a cheap shot.

I'm relatively new to the area so unfortunately don't have recommendations but good luck and it's great you are getting into running! A life-long health positive activity, and DC is one of the best cities for it!