Does the phenomenon described here has a name? Please disregard the political content of the quote, I am not interested in arguing which candidate is better.
Hillary Clinton is the establishment candidate. Therefore, she has far more supporters with loud, influential media platforms than her insurgent, socialist challenger. Therefore, the people with the loudest media platforms experience lots of anger and abuse from Sanders supporters and none from Clinton supporters; why would devoted media cheerleaders of the Clinton campaign experience abuse from Clinton supporters? They wouldn’t, and they don’t. Therefore, venerating their self-centered experience as some generalized trend, they announce that Sanders supporters are uniquely abusive: because that’s what they, as die-hard Clinton media supporters, personally experience. This “Bernie Bro” narrative says a great deal about which candidate is supported by the most established journalists and says nothing unique about the character of the Sanders campaign or his supporters.
The "selection effect" is the name for this effect, viewed very broadly. (That is, there is some process selecting what evidence you see, and you reason as if the evidence you saw was not filtered by that process.)
I'm not aware of a more specific name for the "have you ever noticed that my enemies are mean to me, and my friends are nice to me?" effect besides the standard ingroup / outgroup observations (plus the fundamental attribution error).
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