A haven is a place that is safe. So, "safe haven" is redundant. Shockingly, several state legislatures have even passed laws for dropping off babies with no penalty; these laws are usually referred to as "safe haven" laws.
Safe harbor/safe haven: why the redundancy?
It’s an interesting example of the way language evolves.
Haven: Middle English, from Old English hæfen; late Old English hæfen, from Old Norse hǫfn; related to Dutch haven, German Hafen 'harbor'; First Known Use: before 12th century.
If you argue that harbours and havens are intrinsically safe, it would make the expression tautologous. The earliest sense of harbour in English — in the twelfth century — was of shelter from the elements, which might be an inn or other lodgings. (A cold harbour was a wayside refuge for travellers overtaken by bad weather.) It took another century before it began to be applied to a place where ships might shelter. The verb went through much the same developments. (The sense of sheltering or concealing a fugitive came along only in the fifteenth century.) Haven is slightly older and comes from a different Old English source. Its development is the opposite of harbour — the ship sense came first and the land-based place of shelter evolved from it.
You could have good harbours or poor ones. As a result, English speakers began to attach adjectives to both words to show their judgement of the value of a particular anchorage or port. By the seventeenth century safe harbour was being used to describe one with the needful security.
Both expressions soon began to be used figuratively. In Tobias Smollett’s History of England in 1758: “At length, however, [a parliamentary bill] was floated through both houses on the tide of a great majority, and steered into the safe harbour of royal approbation.”
We retain the idea of a harbour or a haven being a place of safety and security. But a harbour that’s safe from the elements is not always a safe harbour politically, for example in time of war. In the law of the sea, a safe haven is a port in which a ship that is damaged or threatened by the weather may take refuge no matter what its nationality (the alternative port of refuge is now also common).
As a development in legal terminology, in the United States — and possibly other countries — safe harbor means some procedure that affords protection from liability or penalty if followed.
Because of these specialized usages, safe haven has extended senses that means it cannot be said to be a tautology. Beyond that, in general usage, the compounds safe harbour and safe haven have been used for so long that they have achieved the status of fixed phrases. Phrases, in fact, so firmly fixed in our minds that to rail against them is pointless.
As to your shock at safe haven laws... do you prefer to find babies in other, less harboring places?
The phrase "safe haven" is simply not redundant. While it is true that a "haven" is a place that is safe, "safe haven" is an expression that means something different from "haven that is safe". A "safe haven" is a place that is officially designated as safe and whose safety is recognized by law or rule. So far as I know, there is no shorter phrase that means "a place officially designated as safe or recognized as safe".