Nobody is denying anyone the right to free speech here. They're asking someone with a megaphone not to lend it to a loudmouthed asshole. Threatening and organizing boycotts in response to NBC airing something objectionable is exactly how free speech should work.
And in their business they are rewarded by getting larger ratings. If they think this interview will give them large ratings then it is a win for them. Nobody should be telling or asking NBC to do anything that is against its own business needs.
Of course people are allowed to boycott NBC if they want to, but I would rather see NBC air this and see the idiot made into an even larger idiot. Everyone wins.
But there is nothing objectionable in NBC airing this.