"Let's have a conversation on guns, but not let those pro-gun people

have any say in it."

There is no point whatsoever for gun control advocates to engage in discussion with the NRA or its allies at any level. Trying to have a debate with the NRA on this issue is like talking to a brick wall. Doing so makes one frustrated, angry and is ultimately unsuccessful.

As a media organization we don’t usually discourage direct dialogue and efforts at compromise resolution. In this case, however, ostracizing the bully is the only approach that will work; talk show and news program debates are only likely to continue serving as the wrong playing field.

As the man says, sounds like they've realized that arguing emotion against inconvenient facts doesn't work real well; so they want to keep the facts out of the way.  So they don't want the other side to argue AT ALL. 
'Ostracizing the bully' equals 'We don't want to hear your side.'