If we stop messing around in other countries' internal affairs, they'll stop hating us. It doesn't matter if it's Latin America or the Middle East, we just need to stop messing around with them.
Sort of like we didn't mess around with Nazi Germany, Fascist Italy, Fascist Spain, Imperial Japan or Communist Russia (at least initially)? That hands off approach (espoused by the likes of Joe Kennedy Sr, JFKs dad) certainly worked out well for us and the rest of the world.
If we want to stop messing around lets just stop spending billions (if not trillions) of tax dollars on aid money around the world for people who don't seem to much like us anyhow. Lets cut off Africa and Central America from our tax dollars for starters. Lets see where that goes. I'm sure Chavez, Ortega and Castro (to name a few) would love to lose the greenbacks and it if we turned a blind eye to whatever they want to do, it's their countries, let them deal with it, right? We don't need to keep armed troops Korea, bring them home and save some money. The North won't harm them, it's not our business anyhow China? They're our friends, no worries. Heck they even built my Mac! How could a country that mass produces wonderful Apple computers (while brutally beating Tibetan Monks) be bad? Russia? They'd never try to unduly influence the fates of Eastern European countries who desperately want to be free. I'm not talking isolationism here, I'm simply talking pairing back Americas responsibilities around the world, getting out of other affairs and saving us some tax dollars. Heck, the Iranians would never try to cut off our oil supply from the Persian Gulf and lord knows the Saudis, Kuwaiti's, Omanies and others in the area are not at all nervous about them, so we should get out of there too. Pakistan and India want to duke it out with Nukes? Hey, it's none of OUR business, they can't hit us from there (yet). The Taliban and their form of government are just misunderstood by the west. We should get out of Afghanistan and let them sort it out for themselves. If they want to kill homosexuals, repress women and generally live in the 9th century because they think the Koran says so, what business is it of ours?
This is a "****ed if you do and ****ed if you don't" sort of deal. We meddle, they hate us, we don't meddle, they hate us. That's just how it is and has been for the past 60 or 70 years of US foreign policy.