Actually I doubt it has anything to do with Fox News.
Europeans, especially those in the UK, are well aware of your almost none existant gun laws, obsessive religious cranks, your relentlessly rightwing politics despite the fact that the GOP have nothing but barely disguised contempt for half the population, uber expensive healthcare, pointless and costly wars in 3rd world countries, your obesity epidemic, tedious sports, baseball, gridiron, basketball, that almost no other country plays, your fixation with electing 2nd rate celebrities and clapped out generals to political office. Most ridiculous of all is the fact that despite all this and much more you insist on seeing your country as "the shining city on the hill" that the rest of the world is just gagging to live in. Well believe me we're not.
Okay, dissection time. Preface, first. I agree that America is fucked up. We've got a lot of problems, and you've nailed quite a few of them, but you're coming across with just a hint of strawman, allow me to elucidate.
1) Our gun laws are quite lax compared to the rest of the world, but its as much an issue of wrangling with the 2nd Amendment as it is simple practicality. America has a total landmass of ~9.83 million square kilometers. For comparison, England has a landmass of 243,610 square kilometers. We're over 40 times the size of England. Policing that much area on a federal level is very difficult, logistically. Look at Prohibition, we tried to outlaw liquor on a nation-wide level, and we were never able to adequately enforce it. The same would happen if we adopted England-style gun control laws. Criminals already break the laws for robbery, rape, and murder, why would they possibly follow laws against guns?
There's a lot of land, and a lot of places to hide, in America. Its why the drug trade is so prolific, despite the incredible amount of money we've poured into the War on Drugs. Some things work on a federal level, some things don't, which is why we have 3 levels of government. But, even if you had it enforced all the way down to the local level, we need only look again at Prohibition.
It didn't work. People will be bought, people will be swayed, and some simply won't care enough to actually do anything.
2) Every country has insane religious nuts. Or, do I really need to point out the likes of Anders Breivik and the Ayatollah?
3) Obesity is a problem everywhere, not just in America. NEXT.
4) Sports? Really? You're calling our country insane because we focus on sports that most of the world doesn't play? How the hell does that even begin to matter?
5) To my knowledge, we've only elected one celebrity and one general to our Presidency: Ronald Reagan and Ulysses S. Grant, respectively. While Reagan is worshiped by the GOP, pretty much everyone at the time agreed that Grant was a shitty president.
You make some good points, but you make flawed ones, as well. I wouldn't call them strawmen per se, but they're...uncomfortably close, if ya ask me.