Hello! I earned my BA in psychology this year, and so I feel I have a pretty firm grasp on the subject to help you out!
So, the thing is is that there are certain mental illnesses where I do feel like a healthy person would be taking advantage of the mentally ill person if they were to pursue a relationship with them, and then others where I feel like pursuing a relationship would be totally fine.
I feel like if the mentally ill person has an intellectual disability or severe autism, that might not be ground you want to tread. Because folks with an intellectual disability have a significantly lower IQ than most folks, I would consider it akin to an adult taking an advantage of a child because folks with intellectual disabilities might not be equipped to be in a relationship and they won't recognize when they're being taken advantage of. It's the same situation with folks with severe autism, too. While some folks with low-functioning autism might be savants in certain areas (drawing, math), in many other areas--such as maintaining social relationships, difficulties with language, etc.--they may have significantly lower IQs which I would again classify as a healthy person taking advantage of them. I would need more info on this and to brush up on this, but if the autistic person is really high functioning, they might be able to date a healthy person without mishap, but I even think that might be kind of a stretch.
There are other disorders, however, which I feel are fine in most cases for a healthy person to date a mentally ill person. For instance, the most common disorders are anxiety disorders, and I think in most cases it would be fine for someone without an anxiety disorder to date someone with an anxiety disorder, but even then, there are cases where I think it wouldn't be okay. It again depends on the severity of the disorder. I think a general rule of thumb when it comes to considering dating a mentally ill person is whether their disorder is so bad it's causing functional impairment (inability to attend work or school). These types of people are generally in a really bad way, and need help more than they need to be in a romantic relationship. On the flip side, if the disorder is not causing functional impairment, I generally feel as if dating them would be fine--but I would always advise the healthy person to tread carefully and always keep in mind that their partner has this disorder so they can understand why their partner makes the decisions they make.
For instance, a person with social anxiety disorder might not ever eat out because there are so many people in a restaurant and too many stimuluses that would make them nervous. A healthy person should probably respect their wishes if their partner seems really adamant about this and might have a melt down if they have to go.
The representation of mentally ill folks in media has always really interested me because I feel as if they're the most poorly represented people out there as they are often portrayed as crazies or killers when most of them are pretty normal folks who just have issues that most healthy folks can't understand and so I'm always looking for people to do great representation with them!
However, I do also understand that a story doesn't necessarily have to be completely accurate to be good or enjoyable, and something that might be a little creepy in real life, can sometimes seem romantic in a story. For example, One Flew Over the Cucoo's Nest is a really good movie, but of course, it portrays mental illness in a pretty bad and inaccurate way. Similarly, while dating a person with severe social anxiety in real life could be pretty predatory, in a story, under the right circumstances, it could be pretty romantic if done properly. For instance, not everyone really realizes they even have a mental illness, and an interesting way to make a story might be to make it so that the male or female in the story doesn't realize they have a mental disorder and they get married at a really young age and the female (or, a little more rarely and interestingly, male) character can suddenly realize that she's really nervous around folks who aren't her husband and she tries to get a job to find that she can't interact with people without her heart racing, and then her husband can take her to get diagnosed when she has a melt down about how poorly her day went at her job, and the story can be about her husband learning how to love her all over again despite her mental illness. You can explore the mental illness in a really flattering way here, too, because you get to see why the husband would have fallen in love with her in the first place, and that the disorder may have even played a role in why he fell in love with her. For instance, people with anxiety disorders are often brilliant artistically, and maybe that's part of the reason why he first fell for her <3.
Ughhh sorry I REALLY rambled there, but I find psychology to be fascinating and I could talk anyone's ear off about it all day, teehee. Anyways, good luck on your project and don't stress too much about being as accurate as possible because a story can be good and still be inaccurate in my opinion.