Yes and yes.
If your news paper is your property and you decide to try to censor someone it is your right to do so, your still trying to censor someone and that is morally wrong imo. In return because your newspaper is a business, as word spreads that you censor out of opinion people will realize your newspaper is bias and you would lose people buying it that believe censorship is wrong or just want to have differing opinions so they can make their own opinion on the subject.
I would publish my own paper in this situation and it would strive as the readers of yours that believe censorship is wrong stop buying yours and flock to mine where they can print articles calling you an asshole.
So, you could do it but the moral decision to try to censor someone would be on you and it is wrong. You can say its your right to be morally wrong and I accept that, it still does not make it right.