The law is not similar, though - that's the point you're missing (and domesticating the orders of foreign courts isn't as easy as you think even when the laws are similar). Information which is protected by privacy laws elsewhere is not protected in the US. If - for example - one of the Australian posters here wanted to harass me using this forum I could take action against them in an Australian court and an Australian court could issue a restraining order (and they'd be in violation of that order if they continued to harass me) or I could file a complaint under privacy laws and they could be sanctioned by the Privacy Commissioner here, but I could not get an order served on theymos to remove their posts or to stop them from posting because they would not have committed any offence under US law.
Under US law, very few types of personal information are inherently protected. In order to over-ride free speech laws, you pretty much need to establish that another offence under US law is occurring (and even then, your remedies are going to be somewhat limited and expensive to pursue). The reason why organisations like FaceBook will take action against users and remove certain types of content are often found in local law, not US law. FaceBook operates in Australia and has a corporate office here - that makes them subject to Australian privacy and anti-harassment laws so they are generally responsive to complaints filed by Australian users about breaches of local laws because they're potentially liable if they take no action to prevent those breaches.
If an actual offence has occurred, you remedy lies in the jurisdiction where it occurred, not under US law.