No matter what websites telling you that they can ship alcohol to the United States say. Period. End of story. Also illegal to ship across state lines or within a state, for that matter. You can't get liquor from an international source unless you're a licensed importer. And how many people have that sort of license.
What people do is their own business. Absinthe is shipped to the U.S. and some of that absinthe, especially that not shipped by the U.S. Post Office, gets through, but it's still illegal. The absinthe companies paint a rosy picture, and for obvious reasons don't say that what their doing is illegal, but before taking on the risk people should know the other side of the story.
All it takes is a google search including the words alcohol and USPS or alcohol and shipping to find out the truth of the matter.
While the illegality of Absinthe due to thujone is an open question, even if the government ruled that significant thujone levels were ok shipping Absinthe would still be illegal because it's liquor.