The Island/WMG
The scientifically impossible parts were actually out-and-out miracles.
While the movie does begin with the clone protagonists having to outgrow the silly superstitions their keepers instilled in them, the story is certainly far from being a slam against all religion, and even rather friendly to some religion elsewhere. Two particular examples come to mind: the construction worker on the scaffolding after Lincoln Six Echo and Jordan Two Delta survive their pursuers' major property-wrecking attack rather enthusiastically assuring them that "Jesus must love you!" for them to have survived so improbably; later, after learning about (and trying out) the physical act of love with Lincoln, Jordan also concludes that "There really is an Island." (In other words, Heaven really does exist.)
The former example, in addition to being a bit of a Lampshade Hanging on the Plot Armor that ensures their improbable survival, might well be a hat-tip from the creator of the movie (Michael Bay) to his own Creator. In other words, we're being invited to think of the author of the script as being the Deus in the Deus Ex Machina that saves their lives. The latter example, meanwhile, reinforces the idea that, rather than simply throwing away your faith because your former god (Don Creech, billed in the credits as the "God-Like Man") proved to be a false idol, you should go find a real God. The Island, which your keepers promised you was going to be a utopia, turns out to be a scam? Then go find a real island.
Where this all leads is to a philosophical and theological explanation for how Lincoln Six Echo could possibly have obtained memories from the original Tom Lincoln despite this being scientifically impossible. Who says science has anything to do with this plot development? The reason Lincoln Echo Six remembers the boat known as the Renovatio that he shouldn't be able to is because Michael Bay says so. Since Michael Bay, as the film's creator, gets well-nigh God-like powers to make anything happen that he wants, he's decided to grant his characters a miracle. By the Happy Ending, Lincoln and Jordan are on the actual boat from the late Tom Lincoln's memory, and headed out--presumably--for a real island somewhere. If they continue down the philosophical and theological path on which they've started, the film is subtly telling us, eventually they'll find the real God and real Heaven as well.