The Federation has never engaged in the kind of mindless mass slaughter that the Gorn did in "Arena".
But the Klingons have. And the Andorians were at war with the Vulcans for a long time before the UFP was founded. And let's not forget all the slaughters humans have inflicted on other humans over the centuries.
And the word "mindless" is itself a racial slur. They had a territorial claim on the planet, and they defended their territory. Extreme? By human standards, yes. But mindless? Obviously not, because they conducted the operation with considerable cunning and technological sophistication. "Mindless" is hateful propaganda, not fair, intelligent analysis. By using such language, you undermine your own position.
I do not, and never will, buy the explanation that the Gorn were simply defending themselves in that episode. Their attack on Cestus III was brutal in the extreme. As has already been pointed out, the Gorn gave no warning, showed no mercy, allowed no surrender. If the Gorn really *had* been defending themselves, they would logically have allowed the colony to defend ITself.
How is it logical to assume that an alien species would be bound by human logic? The Gorn are a highly territorial species. They felt their territory had been invaded. They retaliated aggressively against the incursion to send a message to the perceived invaders. By their own logic as a culture, there was a reason for it. We may consider their reaction disproportionate and vicious, but the fact remains that they were provoked -- that our failure to understand, or even recognize the existence of, an alien culture and its values led to the conflict. This is what happens in contacts between aliens. They have different values, but that doesn't mean that conflict can't be avoided through mutual understanding.
And the fact remains that, despite that initial conflict, the Federation and the Gorn have maintained good relations for over a century thereafter. They have never gone to war with one another, aside from that one aberration with the Black Crest coup. They have historically maintained neutral or normal diplomatic relations. You can't judge an entire history of interaction by a single incident. Do you still hate Japan for Pearl Harbor? Do you still hate the British for sacking Washington, DC and burning down the White House in the War of 1812? Do you hate the Klingons for invading Organia? Military conflicts in the past don't make it impossible to be allies in the future.