How to write a character that's morally bad?

I am not familiar with your references.

That said, characters can be morally bad for a variety of reasons.

One is simple sociopathic selfishness; they truly do not care if other people live or die, if they get crippled, they feel no sympathy or empathy for the mother that watched her child get run over by a garbage truck, in fact they found the blood spurting from the child's mouth rather humorous.

They. Just. Don't. Care. All people are "things" they use and discard at their convenience. They will rape children. They will throw a victim screaming into a pit to be consumed by alligators, and laugh as it happens.

But as an author, I would use this sparingly. It does happen, that level of criminal sociopathy exists in perhaps 1 in a few hundred people. Their brains are literally missing a few emotional connections that normal people are born with.

A second type are not clinical sociopaths, they are capable of caring for people, but are more selective -- tribal. For example, strongly focused on family, with care dropping quickly outside of family. The man that says "If you ever hurt my daughter -- I. Will. Kill. You. I don't mean metaphorically, I mean you will die. Understand? Welcome to the family."

A third type are just desperate. They don't want to be evil, but they feel they have no choice, perhaps to feed their children, or take care of their mother. A real life statistic: More than half of street drug dealers live with and take care of their mother, and dealing drugs is the only way they can earn enough to do that.

A fourth type are completely moral. They just feel the only way to ensure the moral outcome they believe in is to do immoral things; and if they do not do these immoral things, then the moral consequences will be worse. They are moral relativists; meaning some moral wrongs were less important than others.

Many Germans in WWII were moral relativists, nobly risking their own lives to hide Jews from the Nazis. It was a moral wrong to lie, to forge documents, but not as bad as murdering innocent women and children because they were Jewish.

The same thing was true in America's Slave South. Many white Southerners secretly aided, hid, and protected escaping slaves, because they felt lying wasn't as big a sin as slavery.

I don't know if this helps, but my advice is to understand what type of evil person you are writing, and make them consistent.

I have never played or seen Mouthwashing so I don't know who Jimmy is or what makes them "well written" in your eyes. But I have seen quite a lot of The Amazing Digital Circus, so I think I can comment on Jax's personality and what, in my opinion, makes him a (mostly) well-written "morally bad" character.

(As a warning, the final episode has been out for less than a month so I will try to avoid any major spoilers, but aspects of this analysis will touch on things learned in the final episode. So if you haven't seen the final episode but you still plan to, proceed at your own risk. And obviously there will be spoilers for the earlier episodes as well.)

For starters, let's be clear what "morally bad" means in this context. Jax is not a violent criminal or a sociopath. He shows clear signs of caring for others and their well-being. It's just that most of the time, it's hidden beneath a veneer of cruel apathy. He is also fully capable of making real friends as demonstrated with his prior friendship with Ribbit and Kaufmo as well as his growing friendship with Pomni, so he is not emotionally or morally stunted in any significant capacity. In other words, there isn't anything mental or psychological behind why Jax is the way he is. He's just a jerk.

But the reason many people find Jax endearing (even acknowledging that you aren't one of them) isn't because they enjoy watching him being a bully to everyone around him. It's because there are reasons for why he is the way that he is, and those reasons are strongly hinted throughout the second half of the show. In episode 6, Jax fully admits that he sees the circus as nothing more than a video game, with all the trapped humans inevitably reduced over time to nothing more than one-dimensional archetypal characters. The reason he is a jerk is the same reason why someone playing GTA don't think twice about driving into pedestrians while firing at the cops trying to prevent them from blowing up half the city - why bother with morals when none of it is real anyway?

This is why Jax nearly has a psychotic break after Pomni tries to have a real moment. Every human in the circus has a defense mechanism that allows them to stay sane and avoid abstraction, and this belief is Jax's. But the presence of a truly three-dimensional human trying to connect with him undermines that belief and threatens to put cracks in his carefully constructed reality. To admit the humans around him are in fact complex flesh-and-blood humans (figuratively speaking) is to admit that his carefree antics have actually been hurting real people. And in episode 8, Kinger's lucid explanation of Caine and the circus is the last straw that causes Jax's delusion to fully shatter, which is why he runs away from the conversation and has the panic attack on the railing.

Without going into specifics, in the final episode, we learn even more about Jax's motivations. The reason he created the delusion and puts up walls is deeply rooted in trauma in his past life in the physical world, and even within the circus, Jax has done some pretty awful things that can't be taken back (which is what Ragatha was alluding to in episode 5 when she comments that Jax doesn't have friends anymore). Jax losing his delusion would mean having to confront some pretty terrible truths, and would likely result in him abstracting on the spot (which is implied to have nearly happened in episode 7 during that acid trip segment). This is also why at the end of episode 7, Jax panics and presses the red button - he is terrified of having to return to his "real" reality. Out of everyone in the circus, Jax is perhaps the only human who actually wants to be there, even if only because it's an excuse to not have to confront his issues.

All in all, Jax is undeniably a jerk, but he's a jerk for multiple reasons. Even if someone finds him insufferable, they can hopefully still understand - and, on some level, maybe even relate with - the reasons for him being the way he is.

What all of this is to say is that a well-written "morally bad" character isn't someone who is merely a likable a***ole. What makes an immoral character well-written is the same thing that makes any other character well-written, and that's being grounded in reality by their past and motivations. Bad people and good people both have reasons for being the way they are and doing what they do, and fleshing those reasons out is often what makes the difference between a well-written character and a poorly-written one.

The best way to make an immoral character well-written is by making some core aspect of them relatable. Take MCU Thanos, for example. Obviously most people aren't going to be able to relate with wanting to commit mass genocide, but the idea of there being so many people that there aren't enough resources to go around and the desire to do something about it is easily understandable. The hallmark of a well-written complex villain is someone whose motives are justified even as their actions are fully atrocious, and that same lesson can be applied to non-villainous jerks.

And at the end of the day, there is no rule that an understandable and relatable jerk even needs to be likable at all. Many of the most hated characters in storytelling history also have well-written and understandable reasons for being the way that they are. But not only does that not make them any more likable, it can even contribute to their unlikability - not every relatable human aspect is something that people particularly enjoy being able to relate with. But whether you want an immoral character that people can't help but like (like Jax or Jimmy) or you want an immoral character that people love to hate (like Dolores Umbridge or Prince Geoffrey) will depend on the story you want to tell ad what that character's role in it should be.