How mean/bad/evil can a protagonist be?

So this weekend I showed the terrible Freddy Got Fingered movie to my good friend

I have to say that I've personally never seen him that pissed off at a protagonist XD

But it did make me question something; how many unlikable actions can a protagonist do before he ends up with no hope for redemption in the eyes of the audience?
Because at the start of the movie, both me and him found him annoying, but not enough for us to completely give up trying to hope for him to redeem himself.
It's somewhere at the halfway point when the movie is at the start of it's 3rd act (you know, the part where everything goes wrong and sets up for the climax where everything will be made right) where got REALLY mad and kept repeating the words "This COULD've been a good scene, if it were someone other than HIM!".

But the thing is, as annoying as the event that triggered that reaction was, in hindsight it really isn't any worse than any of the protagonist's earlier actions in the movie.
Which made me realize it isn't so much how unlikable the single action was, but the frequency of those unlikable actions.

There's a trope called "Villain Protagonist" were the Protagonist is MEANT to be the evil guy, or at least ends up as the evil villain through character development.
Obviously that character is MEANT to do evil and unlikable things, yet for some reason it usually doesn't make the protagonist unlikable. It just makes you sympathize with them, and look at them as a tragedy.
That's however because a good Villain will never SEE themselves as the villain.
Even when a Villain outright SAYS they're the villain, in their eyes they don't see it as the wrong thing to do.
In the Dark Knight, the Joker pretty much parades himself as the villain, but he also says things like how he's "ahead of the curve", implying he truly believes that he's the "true face" of Gotham. That deep inside everyone is a monster like him and he just wants to be the example.

So what exactly does the main character of Freddy Got Fingered do wrong?
He's annoying, he's unsympathetic to others, he does actions that he himself believes are the right things to do.
He does pretty much everything a Villain Protagonist does, and yet it ended up making him more hated than even the likes of the Joker.
What does he do wrong?

Well the thing is, he ISN'T a Villain Protagonist. He's a regular Protagonist and the plot is written to show that his actions are the "right" actions.
Karma doesn't work for him. For every bad action he does, no bad action happens back to him. And even IF a bad action happens to him, they're just there to punish someone ELSE while he just sulks for a bit and then goes back to his usual self of annoying others.

The thing is, when you write a Villain Protagonist, you make the audience KNOW you're not supposed to root for them. You make it CLEAR that their actions are wrong.
Even if they make GREAT arguments for it, even if they even make you realize how bad the world really is, you're still supposed to be encouraged with the thought that "But still, their actions are wrong".

When writing a regular Protagonist, it's different.
A regular Protagonist has to be relatable. Even if what they do is TOTALLY different from what more than 50% of the audience is doing, they still have to be written in such a way that people would be able to think "Yeah, that's what I would do too if I wanted to do what he did" or at least "I understand why he would do it".
And you're supposed to root for them to reach their goals.
For all that to happen, the character has to at least have some qualities that you can admire or sympathize.
Give them at least a few small scenes that show that the character at least means well, or that they are learning, or that they are at least making an EFFORT to do the right thing.
Make them fail, and fail HARD, make them fail in such a way that you can honestly say "Wow, I feel their pain", instead of making them seem like whiners for giving up when a small failure happens to them.

So back to the original question; How mean/bad/evil can a protagonist be?
The answer; As mean/bad/evil as how kind/good/heroic that same protagonist can be.
It's as simple as that.

The kinder your character is, the more you can at least forgive them for doing a terrible unlikable deed.
You can forgive a character who once murdered an innocent man for money if that same character ended up feeling guilty about it and helped the man's family grieve over his death before the end of the story.
It wouldn't negate the deed as a terrible deed, far from it, but it would at least give the audience something to think about how the bad action ended up turning the character into a better person.

The character becomes unlikable the moment there's nothing to hold on to reason that "at least he/she means well".
If a movie has hundred small events that show how unlikable the character is, there should at least be two hundred small events that show how likable the character is.
It's not even that difficult. Just adding a scene of the character thinking about making his girlfriend her favourite dish after he hit her for being annoying.
It doesn't even matter if he ended up not doing it, the fact he at least THOUGHT about it would give enough of an indication that he DOES care.

Again, you can make the character do the most terrible of things, as long as they do equally great things in return, they'll be relatable as Protagonists.