All the page numbers quoted are from
The Opinion of the Scientific Committee on Food on Carrageenan EUROPEAN COMMISSION HEALTH & CONSUMER PROTECTION DIRECTORATE-GENERAL (this is a downloadable pdf file)
Carrageenan - is an odd one in a few respects. Claims that it's a proven carcenogen are in fact incorrect from what has been published.
It appears degraded carrageenan (also called poligeenan) may have bad effects on the body...but the degraded product isn't usually found in food grade carrageenan. The EU looked into this very question in 2003. It appears poligeenan causes ulcerations in stomach, whereas food grade carrageenan does not (page 2). One study showed negative effects of carrageenan, while 2 studies using higher dosages showed no increase (Pages 3-4). This does not indicate a link, if there was a link the higher intakes should have provoked higher rates, not no increase in cancer at all! It seems the studies using the higher dosages appeared more vigorous that the one negative study in design (although they were all done on animals, so what that means to humans is questionable in itself). So far there seems no causal link between carrageenan & any cancer. (page 6) There may be some links to poligeenan & health issues, but there is no detectable amount of poligeenan in carrageenan (they did recommend refining the testing technique for poligeenan so they could lower limits to the minimum), but that there is no evidence of negative health effects from carrageenan & no evidence of poligeenan in food grade carrageenan (page 5).
Hopefully that clears that up. It should be noted that this doesn't 'prove' that carrageenan does not cause cancer, just that as far as we know at this time there is no confirmed link & most of the evidence at the moment points towards it being safe.
To be frank there is a concern about carrageenan & baby products as it could cross the gut/blood barrier in immature digestive tracts - I would suggest that maybe people try & avoid giving it to babies as it's an unknown factor in a developing baby. But for any weaned human I'd say it was as safe as can say for now - that may, may not change (we can say that about any food!), but for now I'd say it's on the safe list unless new info comes out.
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Update
I've been looking through some other research material. In most instances in studies researchers use what's called 'ungraded' carrageenan, this not food grade, the poligeenan levels aren't tested & they get bad results. You can only see this if you read every detail of the full studies (it's not even mentioned in the abstracts!). Basically the research is useless (at least in the EU as we have tests in place to keep tabs on poligeenan levels - I'm not sure what the US has in place, sorry). For those in the EU at least these tests show nothing as they use different stuff to the stuff we eat. As we all know the effects of poligeenan & the fact (at least in the EU) we don't eat it, then why not just test food grade carrageenan - it's almost like they are trying to make it look bad, but as far as I know there really are no commercial wars about carrageenan, it's not a huge product like the dairy/soya face-off. It's all a bit confusing...unless they still use ungraded carrageenan in the US of course, that would explain the continued testing? I'll see if I can find a FDA position statement on it.