Why did Gambol have such an issue with the Joker?

The bank that was being robbed at the beginning is where the mob kept their money; the money that was stolen belonged to the mob.

From the script:

Bank Manager: You have any idea who you're stealing from? You and your friends are dead.

And

Gordon: My detectives have been making drug buys with them for weeks. This bank was another drop for the mob. That makes five banks- we've found the bulk of their dirty cash.

Joker also rubs it in Gambol's face that he stole his money:

And by the way, the suit wasn’t cheap. You should know. You bought it.

In-universe, Gambol is meant to represent one of the younger gangs, not the old-world Italian mobsters. He's seen as being more angry and direct than the other gang leaders at the table. They were all likely feeling the same way as Gambol, but decided that trusting the Joker was good for business. Ultimately they were all mistaken, since like Alfred said they didn't understand this man who just wanted to watch the world burn.

The meta-reason I find more compelling: Gambol was played by Michael Jai White, who was also the title superhero in the movie Spawn. Spawn's archenemy is Violator, who is a demon often in the guise of an evil, scary clown. As the Joker is also an evil clown, Gambol's hostility toward him was likely a nod to Spawn.

The way I see it, Gambol just happened to be the guy to speak up first, and it just escalated. Let's walk through their dynamic in this scene:

Edgy clown barges into a meeting full of crime lords dressed exactly like the wackjob who stole their money. It's reasonable for Gambol or any of the other mob bosses to put Joker down. Gambol gives Joker a chance to beg for his life. Joker flippantly suggests a magic trick instead. Gambol sends his right-hand man to handle the Joker, whom Joker KILLS as part of the "trick."

Joker may have impressed the others, but clearly at Gambol's expense. Joker then gloats about the money he stole from them. Gambol gets up to kill Joker but stops out of respect for another mob boss's request to hear Joker out.

Joker starts to explain the deal very disrespectfully, so a vexed Gambol interrupts him: "Freak." Perturbed, Joker goes on to demand a ridiculous fee ("Uh, half") for the ridiculous service of killing Batman. The others laugh it off, but Gambol, in no mood to laugh, calls him "crazy." A little pissed off by that second remark, Joker decides to belittle "little Gambol" by name.

Gambol gets up again and is only stopped by Joker's bombs threatening to kill EVERYONE present. Everyone is scared by or angry at the Joker at this point. Gambol sets a bounty on Joker's head. Anybody could have reasonably done so, but he took initiative because he was insulted the most.