Keep your personal business out of your professional business.

I just have a hard time understanding how people can allow their personal life or feelings to infiltrate their professional life.

For instance, recently a man went on x-factor NZ and a woman, who I'd honestly never heard of before this, named Natalia Kills went on to berate him for his appearance instead of judging him on what she was supposed to: His voice and performance.
She focused solely on how offended she was that someone would 'copy' her husband. (Willy Moon or whatever his name is not the first man to wear a suit and slick back his hair. Nobody copied anything. The guy just dressed formally. If you're going to go on about original looks, you should change yours because that look is not original at all.)
For her unprofessional outburst about something completely irrelevant to what she should have been focusing on, I think she did deserve to get fired. (This isn't even the first time they've acted like assholes. In 2015, Moon allegedly called a woman a "cunt" twice following a traffic dispute. The woman responded by writing an open letter. TV3 issued an apology on his behalf, but Moon refused to apologise, repeating the insult and accusing the woman of lying. His wife then also repeated the insult and accusation. I mean, it's okay to get frustrated by a traffic dispute, but why do you have to have handled it like that? Seriously?)
Another example, that's kind of controversial, is the whole Bill Clinton cheating thing. He had an affair, and that somehow effects whether or not he can run a country?
I feel like what he did should have remained between him and his wife and the woman that he cheated with. Maybe I just don't see how that should have effected his presidency, so if someone knows, can you tell me?

The only situation I can see someones personal feelings being significant in the work place is if there's someone, like a boss, abusing their power or employees and hurting people. Or a fellow employee is harassing you or someone else and causing a shit ton of issues around the office.
A good example of someone who should not be the boss of an office is someone like Andy Bernard from The Office. I know he's a fictional character, but there's gotta be someone like him in the world, and he's not someone who should be someone's boss. He acted so unprofessionally so many times.