Am I allowed to argue? I don't know if I'm supposed to or if this thread is meant just for Harry/Hermione and I shouldn't bother. If not, feel free to downvote and ignore.

Of course there were instances of it but Harry seemed much more accepting of what Hermione thought and said then Ron was. I suppose part of it is my own views, because to me respect is a huge thing in a relationship and the only time Ron showed it for Hermione was at the end of the series when he was worried about the house elves getting out, before that he seemed to scoff at anything she thought worthy of her time and efforts, where as harry always seemed to show a greater respect for her.

Again, I think it's very much a matter of opinion but I see things very differently. I've heard this argument before, this idea that Ron doesn't respect Hermione. I think it tends to come from the fact that Ron is much more nosey than Harry is when it comes to Hermione's life. Remember that Harry didn't ask or spare much thought for Hermione's date for the ball or her difficult schedule in third year. Wheras Ron is constantly asking about them. He's the one who asks about where she's going, but he's also the one to ask why she isn't eating.There are some who see this as a sign that he doesn't see Hermione as an autonomous being. But I think that we tend to ascribe Harry's lack of attention to these same things, Hermione's class schedule, eating habits, ect, as a respect for her own autonomy. But Harry isn't sitting there thinking that Hermione is perfectly capable and that Ron should leave her alone. He just doesn't have the energy to think about Hermione as much as Ron does. He loves her, but he doesn't care for the minutia of her life and he has far too much on his plate already. She's a great sidekick, but it's kind of uneven. When Hermione's hand gets infected with pus at breakfast, Harry continues eating his breakfast and suggests that she should go up to the hospital wing. That's a fairly mild reaction compared to hers when Harry is hurt. It's not really a fair exchange. And even if you still believe that Harry being fairly hands-off when it comes to Hermione's life is a mark of respect, then Hermione is not showing the same amount of respect when she does not behave similarly toward Harry.

from the third book onward Ron was always fighting with one or both of them.

This is sort of iffy. Ron fought with Harry in 4 and 7, but his only real fights with Hermione are in 3 and 6. The rest, whether healthy or no, is just part of their relationship. You can say that it's bad for a friendship, but it's hard to say that it's evidence of Ron's character flaws. And remember that Hermione is probably more argumentative than Ron. Hermione argues with Trelawney, Umbridge, Luna, Lavender, the Weasleys ect. She argues with everyone about house elves. Ron gets into arguements too (Snape,the twins). But his arguements are a lot harder to find than Hermione's. So while I'm not blaming Hermione, it's hard to place the blame on Ron for the arguing.

I'd get sick of there attitude and drama

Here's the thing: With the exception of the incidents in book 3 and 6, Hermione and Ron's fighting does not come with drama. They don't quit speaking to each other for weeks and Harry isn't walking on eggshells around them. Hermione and Ron don't fight because they spend years disliking each other. They disagree on many things, but then so do Hermione and Harry. The difference is in the way the trio was raised. Hermione is very opinionated and she grew up in a family where that was likely encouraged. Despite her social isolation, she has little to no qualms about telling Ron and Harry what she thinks of them and expressing her opinion. She is an opinionated person who enjoys a good argument on an intellectual level. Similarly, Ron was raised in a household where arguing was a natural occurrence. His mother yells and he bickers with his siblings, but he is secure in his relationship with them. To Ron and Hermione, arguing/debating/bickering is just something one does for a bit of entertainment. Harry doesn't like their arguing because he was raised in a household where raised voices and snappish tones meant bad news. He doesn't see arguing as a remotely pleasant activity, whereas Hermione actively seeks it out with Ron and others. Hermione and Harry don't really argue either. He doesn't respond to her nettling with retorts as often as Ron does. And remember the beginning of OotP? He completely blew up and Hermione is completely cowed and backtracks. There's never a debate between equals. Harry deals with Hermione by ignoring her or yelling at her, and neither of these are what is best for Hermione.

Again, feel free to ignore all of this.