I said in a previous question that my protagonist "is a very shitty person that makes bad decisions for the wrong reasons". My antagonist, however, is a good person trying to do what they think is right, but opposes the protagonist. How do I make the audience root for the protagonist?
Be careful not to confuse the concept of protagonist with the concept of good guy or even hero. Protagonist simply means the main character of the story. Similarly, antagonist does not mean bad guy or villain, it simply means the person opposed to the protagonist.
There is nothing at all to say that the protagonist has to be good and the antagonist bad. It is certainly the more common setup, but there is nothing that requires it.
Nor is it essential for the audience to root for the protagonist. Do we root for MacBeth? For King Lear? For Othello? For Raskolnikov, For Miss Jean Brodie? What is essential is that the audience be interested in the protagonist. We may wish for the protagonist's downfall and still be more interested in their story arc than that of their virtuous antagonist.
It can be just as compelling to have the reader rooting for your protagonists defeat, or for their reformation, as for their victory. In many ways, the reformation of a bad protagonist is more moving than the victory of a good one. Redemption is one of the most profound themes in literature.
But you don't even need that. There is no one worth rooting for in On the Road. It is basically a horror show of cruel and self-destructive hedonism. There is no redemption to be found in it. But it is compelling stuff nonetheless, because in these horrible people we recognize humanity and its struggles. We may, perhaps, hope for a redemption or a comeuppance, but neither ever comes. It ends in exhaustion and estrangement. If there is a payoff, it is that the world stops spinning and the music stop blaring and you can think again. It is a horror show, but it is a compelling horror show.
You can't get your audience to root for a character they fundamentally don't like. If you try you risk running into the Designated Hero trope where the only reason we are expected to treat a character as a hero is because we are told to by the author.
Tropes aren't inherently bad if used properly, of course. You could argue that Deckard, the protagonist of Blade Runner, is a designated hero. We follow events from his point of view but he's an alcoholic, he treats women terribly and there's no getting around the fact that his job is killing beings that are indistinguishable from people for money. However it works in that setting because a) the whole work is deliberately morally grey (the antagonist only wants to live, and he only commits one completely unjustifiable act during the entire film), b) his opponents utterly outclass him which makes him relatable because everybody loves an underdog, and c) Deckard has qualities that can make him relatable and even likeable to a degree, for all his flaws. His determination is admirable and he's obviously also very good at his job regardless of how morally dark that job is.
If you want your hero to be a jerk and the villain to be better than him, then you could consider character growth as a possible way out. Just because your character starts off as an unlikeable jerk doesn't mean it's impossible for him to learn the error of his ways and tone down his behaviour. If he makes bad decisions he should suffer negative consequences for those decisions. More importantly he should learn from those consequences so when confronted with a similar situation in the future he doesn't repeat the same mistake (though you could have him make a completely different mistake if you want him to have to learn his lessons the hard way). An audience can really bond with a character that exhibits the ability to recognise and rectify his own flaws.
Not So Good Guy as Protagonist
You may find some value in looking up the anti-hero or even villain tropes. Having murk in your story which prevents people from easily deciding who is right and who is wrong is totally fine and at times really interesting; but you're not going to win over an audience to like an unlikable character over a likable one; it's right there in the definition.
There are stories where we root for the bad guy, even if its only in a specific set of scenes. Generally this is because the "unlikable" character is still a proxy for some sort of wish fulfillment, or redeems themselves. Inherent to a successful story that attempts any of this is your ability to earn the readers trust, which typically means defining motivation for your character very very well.
If your characters are internally consistent and do things that make sense for what they desire, then they can be unlikable. But, if your foil and antagonist is a do-good likable character, you're going to need to have a scene where the "unlikable" character does something that differentiates himself; normally this means doing something that only he can do since he is unshackled by the concerns of the standard good guy. It also doesn't hurt if there's some aspect of the persona that forces the reader to like that character more than they should. A sense of humor goes a long way.
Look at some popular anti-heroes & villains: Deadpool, Hook (Good Form/Bad Form version), The Joker, Hannibal, Han Solo (The One Who Shoots First), Malcolm Reynolds, 'The Bad' & 'The Ugly', and anti-hero etc & villian etc.
What do these characters have in common? They have a vision of who they are; they have good internally consistent reasons to not be the good guy; they are, in some respects, unexpected given the medium they show up in; they are the reason you watched that movie they showed up in. There are a lot of these types of characters in books to. Dragonlance's Raistlin is not a good guy, and yet the reader wants to know what's going on there. A healthy dose of mystery in this case goes a long way. The other thing almost all of these characters have is a foil. (Deadpool's foil is all of those other superhero movies, they don't actually have to show up in his given how prominent they are in our culture).
Based on your questions so far, I would go so far as to suggest there may be another question you need to consider:
What is the point of this story?
It sounds like, maybe, you have more of a collection of people, events and things; and not what Western society would consider a cohesive story. Maybe you have a lot of good elements, but they aren't strongly tied together. Your motivations for your characters may be weak. Or, you may not have constructed a story that earns the reader response you are looking for. I once had a professor hand me an essay back and he said, "You like to put all your ideas on the ceiling, like a kid with a bunch of spit balls; but at some point, you need to scrape the ones off you don't need." A story is more than just a collection of people and events, it is a collection of on-point things that work together to create the atmosphere, tension, and release that engage your reader.
When your characters serve to fulfill the promises you're making in your book, and are internally consistent they work out a lot better. My guess is that you've pantsed your story (written it down without an outline, generally making it up with only a loose idea of where it was going). In which case its now time to figure out what your story is about and potentially you may need a redraft of any of those characters, beginnings or endings so that they create the story you wish to tell. Determining whether something works should be as simple as asking others to read that can give good feedback. Fixing it is going to require understanding what it is you actually want your story to accomplish. I would posit that if you're telling a story about a character who is "a shit," that your promise might be "sometimes it takes a shit to get things done." In which case you need to figure out how to establish that's what your story is about early enough that you don't lose your readers.