Starting at Wikipedia, we see that the keffiyeh is of course not "Palestinian" at all, but Arab, meant to shield the head from the sun and sand. PalArabs did make the black-and-white version symbolic, which makes one wonder if they are as aghast at the Jordanian red and white version as they are at the modern Jewish blue and white version.
A paragraph in the Wiki entry, no doubt written by an angry Mizrahi Jew, says:
The tribes of Israel, and their Jewish and Samaritan descendants, have worn variations of the keffiyah since biblical times. This practice was not unique to the Arabs, as the wearing of headgear is a universal practice amongst Semitic peoples and a logical protection against the harsh mid-east sun. From the biblical and rabbinic sources it can be deduced with certainty that the ancient Israelites wore headgear similar, if not identical, to the Kefiyah (كوفية) still worn by Arab and other Semitic peoples. Variations of the Jewish Kefiyah (كوفية اليهود ), also known as a Sudra, were worn by middle-eastern Jews from ancient until modern times. This ancient practice rapidly declined with the founding of the State of Israel and the false association made by some racist European Jews of the keffiyeh (كوفية) as a solely Arab clothing item, rather than being an authentically Jewish practice and custom.The Talmud does mention the "sudra" a number of times, and Jastrow translates it as a scarf wound around the head and hanging down the neck or a turban. It is clearly a head-covering that one ties on (Berachot 60b). A passage in Kiddushin 29b implies that only married men wore it.
No proof was brought that it was worn in biblical times, although almost certainly some sort of cloth headcovering was. It is possible that more elaborate turbans were reserved for prominent people.
Either way, Jews were wearing a variant of the keffiyeh many centuries before anyone ever heard of "Palestinians." Which makes the claim that Jews are "stealing" parts of Palestinian Arab culture even more absurd than it already was.