and any such claim immediately indicates woo-science. It may mediate against the effects of radiation but protect - no.
Now onto the "hundreds of studies in peer reviewed journals". Any citations to support that? Nope.
There have been some studies of Fucoidan. In vitro (under glass) it seems to have an effect on some cancer cell lines (1) but this has not been replicated in vivo (in a living organism).
There have been small in vivo studies with rabbits which seem to show an effect on hyperplasia (rapidly proliferating cells) (2) but these have not been effectively replicated nor has a mechanism been identified (3)
There was a clinical study which showed an increase in CD34+ immune cells and expression of a cell binding factor (4)
On the other hand there was the experiment with rats that showed that Fucoidan increase mortality from meningitis (5)
As to the super long life of Okinawans, well they don't live that much longer. Currently their average lifespan is about 1 year longer than mainland Japanese (and that only since about 1973) and about 2 years longer than Swedes. More likely it is not a magic ingredient which supports this life span but the generally healthy diet including lots of fish and very less pork and refined rice.
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(1) Aisa Y; Miyakawa Y; et al. (2005 Jan). "Fucoidan induces apoptosis of human HS-sultan cells accompanied by activation of caspase-3 and down-regulation of ERK pathways". American Journal of Hematology 78
(2) Jean-François Deux; Anne Meddahi-Pellé; et al (2002). "Low molecular weight fucoidan prevents neointimal hyperplasia in rabbit iliac artery in-stent restenosis model". Arteriosclerosis, Thrombosis, and Vascular Biology 22
(3) Wu XZ, Chen D (September 2006). "Effects of sulfated polysaccharides on tumour biology". West Indian Med J 55
(4) Irhimeh MR, Fitton JH, Lowenthal RM (2007 Jun). "Fucoidan ingestion increases the expression of CXCR4 on human CD34+ cells". Exp Hematol 35
(5) Brandt CT, Lundgren JD, et al. (2003). "Pretreatment with fucoidan promotes lethal infection in a rat model of experimental pneumococcal meningitis". Interscience Conference on Antimicrobial Agents and Chemotherapy