Huh?
I mean, I would have my protective instinct triggered when people they I actually know and care for are under danger, and not randoms lol.
But, I would still agree that Garp not even raising an opposition to this atrocity was out of character for him. Maybe he did offscreen, who knows? But at the end of the day, he is one man and can't stop this by himself.
Garp is one of the best characters in the series, a true embodiment of internal conflicts - conflict between what his heart desires vs what his brain tells him to, conflict between loyalty to his ideals vs loyalty to his family.
In Marineford.
His brain tells him that Ace made his own bed (which Ace himself tells Garp), so Garp at least nominally defends Ace's execution. He prevents Marco from saving Ace due to this reason, because he made up in his mind that Ace was executed. He sees no other way.
This is why he stands in Luffy's way as well, but unlike against Marco, he truly couldn't bring himself to punch the shit out of Luffy. Exemplified perfectly by the panel of him closing his eyes at the last moment, probably turned off his haki too.
When Ace was finally freed, came a glimmer of hope in him that Ace was to be saved. And when Akainu killed Ace after this, when it was least expected. Garp lost all his reasoning and snapped, he was at this point only controlled by his emotions and hence asked Sengoku to keep him down.
In this manga where most characters lack any internal conflicts, where good guys don't face the consequences of their actions. Garp stands out spectacularly.