Why Renly wasn't "playing at war"
I've seen many people describe Renly as essentially a male version of Sansa, i.e an entitled and sheltered airhead who held romantic ideals about the world, and didn't understand the horrors that exist in it.
This post is about how that isn't neccesarily true, but is just the surface appearance of Renly.
First of all, the two sources that show Renly in this light are Catelyn, who has the wrong ideas about Renly, and Cressen, who probably sees Renly as a young boy still because he raised him and last saw him when he was 8.
This is madness, Catelyn thought. Real enemies on every side and half the realm in flames, and Renly sits here playing at war like a boy with his first wooden sword.
They are still unblooded, Catelyn thought as she watched Lord Bryce goad Ser Robar into juggling a brace of daggers. It is all a game to them still, a tourney writ large, and all they see is the chance for glory and honor and spoils. They are boys drunk on song and story, and like all boys, they think themselves immortal. (ACOK, Catelyn II)
Catelyn thinks Renly's knights are "knights of summer". She is frustrated by Renly's slow progress, thinking he's playing at war. She's right about Renly's followers, but as for Renly himself....
He feasts every night in a different castle, and hold court at every crossroads he passes …were I he, I would do much as he is doing. Make my progress, flaunt my power for the realm to see, watch, wait. Let my rivals contend while I bide my own sweet time. If Stark defeats us, the south will fall into Renly’s hands like a windfall from the gods and he’ll not have lost a man. And if it goes the other way, he can descend on us while we are weakened. (Tyrion IV, ACOK)
Renly's slow march was in fact an effective twofold strategy, as Tyrion mentions he was letting the Lannisters and Starks fight each other, and at the same time had blocked the supply of food to King's Landing and was embargoing it from a distance. This would ensure that the city folk would riot against the Lannisters and when Renly arrived with all the food from the Reach, he would be welcomed as a hero (even though he was the one who starved them in the first place!) His tourneys and feasts also held a higher purpose than mere entertainment, they kept his troops occupied and in high morale, and sharpened their fighting skills.
Looking at Renly's behaviour, it's clear that he's actually a shrewd politician who knew the world he was living in.
"Strike! Now, while the castle sleeps." Renly looked back at Ser Boros again and dropped his voice to an urgent whisper. "We must get Joffrey away from his mother and take him in hand. Protector or no, the man who holds the king holds the kingdom. We should seize Myrcella and Tommen as well. Once we have her children, Cersei will not dare oppose us. The council will confirm you as Lord Protector and make Joffrey your ward." (ACOK, Eddard XIII)
If he was truly naive, he wouldn't see the danger the Lannisters posed to him and cut his losses and flee the capital, instead he would assume he could go on living safely in KL.
"I have twice that number here," Renly said, "and this is only part of my strength. Mace Tyrell remains at Highgarden with another ten thousand, I have a strong garrison holding Storm's End, and soon enough the Dornishmen will join me with all their power. And never forget my brother Stannis, who holds Dragonstone and commands the lords of the narrow sea." (ACOK, Catelyn II)
It could be said he shows naivety here, by assuming Dorne and Stannis would join him, but I'd argue that it's just him deliberately overselling his own strength to Catelyn in order to intimidate her, as he goes on to subtly threaten her:
Wherever she looked, she saw fires. They covered the earth like fallen stars, and like the stars there was no end to them. "Count them if you like, my lady," Renly said quietly. "You will still be counting when dawn breaks in the east. How many fires burn around Riverrun tonight, I wonder?" (ACOK, Catelyn II)
And later makes her stay behind and watch the battle as a message to her son about what happens to those who oppose him:
"My lord," she announced. "If you are set on battle, my purpose here is done. I ask your leave to return to Riverrun."
"You do not have it." Renly seated himself on a camp chair.
She stiffened. "I had hoped to help you make a peace, my lord. I will not help you make a war."
Renly gave a shrug. "I daresay we'll prevail without your five-and-twenty, my lady. I do not mean for you to take part in the battle, only to watch it."
"I was at the Whispering Wood, my lord. I have seen enough butchery. I came here an envoy—"
"And an envoy you shall leave," Renly said, "but wiser than you came. You shall see what befalls rebels with your own eyes, so your son can hear it from your own lips. We'll keep you safe, never fear."
There's also this from Loras:
He said that all his other knights wanted things of him, castles or honors or riches, but all that Brienne wanted was to die for him. (ASOS, Jaime VIII)
So Renly knows people aren't following him because he would make such a cool and awesome king, but because they want favours from him.
He also wants renowned knight Barristan Selmy on his side as he is a valuable political symbol, something Cersei failed to understand when she let him leave King's Landing.
Renly nodded. "See to your battles, my lords . . . oh, and if Barristan Selmy is at my brother's side, I want him spared. (ACOK, Catelyn IV)
But at the same time, he understands the danger of keeping Stannis, a rival claimant to the throne, alive.
"When my brother falls, see that no insult is done to his corpse. He is my own blood, I will not have his head paraded about on a spear." (ACOK, Catelyn IV)
His Rainbow Guard's bright colours, although ostentatious, is a homage to the Faith of the Seven, which would help in Renly's image politics.
Lastly, "Renly knows nothing of war or hardship" simply cannot be argued, because of this passage:
"Well I remember." Renly lifted his chin to allow Brienne to fasten his gorget in place. "Near the end, Ser Gawen Wylde and three of his knights tried to steal out a postern gate to surrender. Stannis caught them and ordered them flung from the walls with catapults. I can still see Gawen's face as they strapped him down. He had been our master-at-arms."
Lord Rowan appeared puzzled. "No men were hurled from the walls. I would surely remember that."
Maester Cressen told Stannis that we might be forced to eat our dead, and there was no gain in flinging away good meat." Renly pushed back his hair. Brienne bound it with a velvet tie and pulled a padded cap down over his ears, to cushion the weight of his helm. "Thanks to the Onion Knight we were never reduced to dining on corpses, but it was a close thing. Too close for Ser Gawen, who died in his cell." (ACOK, Catelyn IV)
By Renly's own admission, as a child he witnessed his Master-of-Arms being strapped down to a catapult to be thrown over the walls, overheard a conversation about cannibalism, and likely had to eat rats or his own pets along with the starving garrison while the Tyrell forces feasted outside in hopes that the men around him would betray him and kill him. That sounds a lot worse than Bran watching a guy get his head chopped off.
TLDR; while being a "knight of summer" can be argued for Loras and Brienne or Renly's supporters such as Robar Royce, it doesn't hold true for Renly, who was actually quite self aware, ruthless and politically minded.