I disagree. Now I'm not saying his characterization post death is solely due to his feelings towards Aerith, nor have I ever, but there is definitely some overlap. Advent Children shows that. As does OtwtaS
In what sense? In advent children especially his personal feelings for Aerith are completely irrelevant, if anything they serve only to muddy the waters. Advent children is a continuation of Clouds issues concerning fear of failure, his guilt concerning his failures of the past (specifically in regards to Aerith and Zack), his shame about being happy when they are dead, and his own coming death, aka his upcoming failure to protect people yet again.
These issues there are about Cloud, not Aerith, the problem with adding in romance as a contribution factor here is that the story works perfectly fine without it, adding in romance adds nothing of value, all it does is detract from what is actually being explored through the story.
There is a question here that the viewer tries to answer. That question being: "why is Cloud so haunted by Aeriths death?". And by answering "because he loved her, you've now created an extremely shallow and cliché motivation that serves to hide the actual answer. It no longer becomes a story about who Cloud is, but about who Aerith was to Cloud. By doing so you rob the story of the very thing that gives every story its depth, the exploration of humanity.
When you say "Cloud is this way because he lost 'the girl he loved' " you add in an implication that he would not have acted the same way had it just been a friend, which in turn assassinates Clouds character. Which is what leads to a lot of the complaints that you hear about Cloud in advent children. That he's an edgy asshole who abandoned Tifa to go sulk in a church. And in this characterization, they're right, Cloud is an awful character in this telling of the story, because the only thing this story tells us about Cloud is "Cloud is the kind of guy who gets very sad when the girl he loves dies, so much that he will abandon his girlfriend and his kids to sit in a church and wish for death so that he can be with his deceased lover".
It's a revolting story that romanticizes depression and makes the hero irredeemably awful. This Cloud would allow children to die because he's sad his girlfriend is dead.
Ofcourse, this isn't the real answer, even IF Cloud had romantic feelings for Aerith they have nothing to do with his actions in advent children. The problem is that by postulating that the feelings exist you automatically create the assumption that these feelings are relevant, why else would they be there? This is a version of Chekovs gun, the thought goes like this: "if something is in the story, then it must have relevance, otherwise why would it even be there?". So the belief that Cloud loves Aerith leads to the belief that those feelings are what cause his actions in AC, which leads to the destruction of Clouds character, struggles, and character arc.
Regardless of whether Cloud is in love with Aerith, the answer to "why is Cloud so haunted by Aeriths death?" is that "he blames himself for it". His failure to protect Aerith is the culmination of a story arc that started all the way back when Tifa fell into a coma and Cloud blamed himself. The answer is that Cloud failed to protect Tifa as a child, was blamed by her father, and blamed himself, he then thought that by getting stronger he'd get her to notice him, he made a promise, then he failed to become a soldier, then he failed to save nibelheim, then he failed to save Tifa from getting stabbed by Sephiroth, then Zack dies because of him. And after all this failure lead him to develop an alter ego that was everything he wished he was, a hero, a soldier first class, he still failed at saving Aerith. Everyone is dead because of him and yet he's still alive, and happy, and it's eating him up inside, he feels like he shouldn't be allowed to be happy when they are dead. He hates himself, and his weakness, his incompetence, his incompetence that gets people killed.
He tries to atone, THAT is what we see in otwtas, he tries to atone through Denzel, but Denzel gets geostigma and will die, Cloud has failed yet again. He tries to atone through living, and we see him succeeding at times, it's even stated that he's happier than ever living with Tifa, but that this makes him feel guilty, as well as anxious about losing said happiness. Things get better though, as stated in OTWAS, however, suddenly Cloud leaves....why?... Because ultimately he himself gets geostigma, which to Cloud means failing again, whats more a failure he can't get back from. He can't protect his family, he will leave them behind. It's this self hatred, this guilt, this utter dejection that motivates Clouds actions. The reason he refuses to go save the children is because he legitimately thinks that he can't save anyone, as he explicitly states in the movie, that's not about Aerith, that's about Cloud. He's not in the church because it's a happy place that reminds him of Aerith while with Tifa he was miserable, no, he's miserable in the church, that's why he went there, because he hates himself and has given up and will now accept dying as punishment for not being able to atone in life.
Cloud in Advent children is a hauntingly realistic depiction of depression, feelings of inadequacy, survivors guilt, and a host of other issues, and the implication that what's really going on is that he's 'love sick' just makes a mockery of that. I really don't see how anyone could think the addition of Cloud having feelings for Aerith would somehow benefit the story. I don't even know what they're proposing as a character arc here, that story has no middle and ending, it supposedly starts with him pining about being with Aerith after death, and ends with him pining about being with Aerith after death, the growth supposedly being that he's now enjoying his time till he gets to die or something.
I could spend hours more talking about all the symbolism and meaning in Clouds character arc in AC that is lost when you suppose romantic feelings, but I think that would be counterproductive, what matters here is what I said earlier, namely that this is the story whether Cloud was in love with Aerith or not, his feelings for her change NOTHING..... EXCEPT that it makes people misunderstand Clouds motivations, which then leads to the collapse of the entire story as I laid out.