That's the rub: people often think that RFK was some sort of martyr for Israel. Unfortunately, the facts get in the way of that sort of kumbaya feeling. All the presidential candidates were pro-Israel, certainly more so Hubert Humphrey and Nelson Rockefeller. There's a backstory to his donning that skullcap in Oregon that's too long and somewhat irrelevant to the OP to discuss at length. Needless to say that his attitude often drifted closer to George H.W. Bush's than Dubya's: negotiations and the '67 borders not being permanent. That's just the public stuff, BTW. Not to say that he wasn't pro-Israel: but no more than the average US politician of similar rank and stature, if anything a bit less.
Needless to say Sirhan did not have support: all the Arab countries condemned it, his own father said he should be hanged for it (thank SCOCA for striking down the death penalty in '70- Reagan never modified the method from electric chair to lethal injection for some reason), and the UN flew its flags at half-mast for a mere presidential candidate. It was an act by a lone loon who wanted to be famous by killing a celebrity. Sui generis.
As for the act itself: there's really no dispute. It doesn't take a rocket scientist to shoot an unarmed civilian in a dimly lit, confined space from within 10 feet. Even then, had he not stabilized his elbow on the cart it would've gone wild and missed. Hell, even IOTL 1/2 inch further back (which means that the bullet doesn't shatter along with bone fragments into the brain, but hits the hardest part of the skull- inpenetrable by a .22 peashooter- in the back) would just mean 3 weeks recovery time before hitting the trail again.