I'll disagree with John Quiggin on this one. He seems to think the statement, GMO foods are unhealthy, is too broad to be refutable, and therefore people who believe the statement aren't showing epistemic closure. The problem is that AFAIK there's no evidence to support the statement, so people who are convinced of it in the absence of evidence are showing a certain close-mindedness that's evidence of epistemic closure. I guess I should hasten to add that I'm no close follower of the field, and I do vaguely recall concerns that gene transfer from allergenic species to non-allergenic species could be dangerous to some people, but there's almost nothing to back up the statement.
There are more valid reasons to be concerned about GMO foods, especially contamination of wild varietals, but the health issue isn't a good one. Nothing like the level of closure that we see on the right, but it's still there.
UPDATE: See the comments - John says we may not be in disagreement on the broader allegation over whether GMO foods are unhealthy.