Keep in mind I could be completely wrong(probably am), but I've always thought of Rhaegar as a broken human being. He was born while Summerhall and many of his relatives were turning to ash, witnessed his father abuse his mother in many different ways, with the worst being the rape, while everyone around him pretending it's ok or nothing can be done about it. He was born into royalty so that already twists your logic and messes with your perception, but also born out of incest from a dynasty of incest practitioners, and if that isn't enough his father inherited the typical targ attitude of we're special and I'm great no matter what. These things combined like that and spread out over time made Rhaegar into what i interpret him as.
I believe he had trouble with empathy and of understanding people beyond surface level. It seems to me he embodies the charming sociopath stereotype that is kinda based in reality, with him doing what he thinks he should do based on what society tells him is good. He uses societies rules as a guidebook to read off when his charm and observational skills fail him, and tries to be the best of what his guidebook tells him is good. When he found that damn prophecy suddenly everything made since to him, why everyone is so confusing and why he feels different to everybody else; 'he's special and destined for great things like saving the world'. I interpret alot of his behavior as him not feeling what others say he should and struggling to understand other peoples lives and fails to see them as fully autonomous. To him it's like everyone is puppets in a big show moving around and acting out scenes but not real, not like him, not special. To him the prophesy explains all this to him, because now he knows life to be a play, a story, a song, in which he is the main character doing the good thing so all the other characters can live, and that will make him good and right like he's supposed to be. It makes his condition righteous and justifies whatever he has to do so that he can fulfill his destiny.
Then he meets Lyanna, who's different but that makes sense right? Rhaegar is different so why wouldn't she be too? Oh more of the prophesy suddenly makes sense now doesn't it? Ice and fire, Stark and Targaryen. They are meant to be, to make a special person who can save everyone. Cue obsession to make more of his life make sense to him by wooing the person who is also different. He has paid attention to the people around him all his life so he knows how to act and blend, and knows that many maidens like certain things so he will do those things with Lyanna. Offer her things that she would like, such as the freedom from her betrothed. It's okay he doesn't need the guidebook anymore, they're special and important to the song, so what does it matter what others will say and do? They were made for this.
Oh suddenly everyone is angry and there's war everywhere. Oh why is Lyanna crying and wanting to go home? Doesn't she know how important they are? Our babe is going to do be a queen and a hero unlike any before her. I've told her this but she just cries harder and flinches from my touch, and looks at me with so much horror and confusion. I can fix this. I can make her understand. First i have to win this war and i will win, it is my destiny, then i will overthrow my father and make everything the way it is meant to be.
Basically if you didn't catch my meaning, my opinion of Rhaegar is complicated. I see him as a mixture of broken child, quiet arrogance, and hero complex. If he never found or heard a peep of that prophecy he might have been a decent king, certainly better than his father. He would always struggle just like most people with 'empathy disorders', but I don't see him being straight up evil or cruel and callous. He would be the king that would try very hard to be perfect and make everyone happy because those are the rules he built for himself out what people say is good, but eventually I think people would realize just how little he understands and how little of himself there even is. The prophesy is basically his kryptonite.