I try as hard as possible not to be judgemental towards incompetent colleagues, motivating myself with the knowledge that we were all incompetent at some point, and that people need a chance to learn, and that sometimes too much pressure will lead you to believe that they're bad. Or sometimes, people just aren't good at the stuff you want them to be good, and you just need to discover that niche where they will be very useful.

Mostly that goes well.
I've had the incompetent late bloomer who was a family man who started too late to dev, and wasn't really serious. A bit of harsh talk, some soul searching over a few beers, made him into a really valuable asset. Not the brightest rock, but reliable, steady-paced developer who earned his stay.
Then there was the girl who wasn't really good at coding, but saved our team from disaster many times by keeping things into account, and realizing what must be developed or tested at every step.

However, there are exceptions. I've worked with people who have been nothing but a menace, through their incompetence AND attitudes.

The most noteworthy example was an intern that we sought out, by talking to professors to point us to their best students. So we got that intern on board. He seemed strange at first. Kind of perfectionist. Talked serious, with an air of royalty, and always dressed sharply. He really gave the impression that one must be worthy to receive his blessing. The weirdest part was his handshake. It was as if he was touching an iron hand heated to 3000 degrees. It was over before you even knew it. Leaves you kinda offended. Especially when he always took a wet wipe after that and wiped his hands. Am I really that gross?
But that's fiiiine. I mean we're all different and weird in our own ways, right? So he's a germophobe, so fucking what? We just gotta find a way to work together, right?
WRONG.
As soon as he started (and remember, he's a paid intern, who barely knows how to code, and has zero industrial experience), he started questioning my architecture solutions, code implementations, etc. I don't mind discussion and criticism, which is why I welcomed his input. But it seemed like he wasn't willing to accept any arguments, so I started looking for excuses not to talk to him.
Meanwhile, the most productive team member we had, to whom you could just give and describe an idea, with architecture and stuff, well, and you'd see it implemented the next week, with only the most well placed questions asked, started going into fights with this intern for the same reasons I was avoiding him.
.....
And here's the kicker.
Get this:
This intern comes to me (I was the team lead), while that guy is not in the office, and with a straight face, dead serious, starts telling me that that guy was making stupid decisions and being a bad team member because he doesn't ... I quote him almost verbatim... "follow my indications". He said that I had to do something because he refused to work with him together.
I was stunned.
This good for nothing imagined superhuman, who was completely useless and an amazing annoyance to pretty much everyone in the team, came to me, telling me that the most capable and productive developer in the team is bad, because he doesn't follow his orders, and that I had to pick between the 2.

I couldn't believe what I had heard.
I had so much emotion in me right then. I was angry, but at the same time I could barely abstain from laughing.
I just told him calmly that he was wrong, and that I wouldn't mind if he never came back. I didn't see him for 5 years after that.

Anyway, later that week our team went for a dinner + beer, and the stories from all the team members started pouring in. They didn't want to talk him down either, but now that he was gone, it was a weight off, and everybody could tell their story.

What a fucking asshole.

So 5 years after I stumbled on him as he was entering a church. Still an arrogant bitch. Barely exchanged 10 polite words and I continued on my way as he was disinfecting his hands from my filthy handshake.

Socket IO released a major update not 8 days ago. I spent an hour getting a "400 Bad handshake method" until I discovered my server had updated to 3.0.1 but my client was still in 2.3.0.