I believe Renly is a very well WRITTEN character. There is much complexity to him, between his political decisions, popularity in Westeros, looks, sexuality, flaws and virtues. There are times he behaves in a very egotistical manner, and on the other occasions he's very charismatic and "fun to be around". And there are other characters opinions on the man, but frankly we lack source material to learn in-depth about him, as we do with Eddard, Robb or Stannis. There is much ambiguity in Renly, that's why we're discussing him years after Melisandre zapped him in ACOK.
So, a well written character, unfortunately we didn't get to see him as much as I'd like to. That must be part of his appeal, tho.
When it comes to actual Dislike in the community, I think several factors hurt him in the long run:
Poor TV show portrayal. Renly's got very little screen time in HBO GOT and he's far from cunning/wiseass playboy of King's Landing, as we see him portrayed in the books. They failed to address complexities mentioned in this thread and simply went for an "average weakling" who happens to know a man or two.
His role has ended - for good. Stannis campaign Stormlands/Crownlands and the titular Clash of Kings are over. Margaery and his backers (in the books) have their own set of problems. He had no offspring. The tides of history moved on and there's hardly anyone mourning him now, except those two who loved him dearly.
There is no Fandom "faction" around Renly. Holy cows (Dany, Jon, Tyrion, Arya) always had plenty of supporters. House Stark, Targaryen, Lannister or even Martell are popular as a whole. All Baratheon sympathizers (I'm one of them) are more interested in Stannis arc or even Robert's Rebellion. Why is that? Lack of POV chapters!!!
If anyone in the Reach was a POV during AGOT & ACOK, it would be different perhaps.