The Short Version
This claim is false. Major health authorities including the EPA, FDA, and NHS do not advise pregnant women to avoid crab. The EPA-FDA explicitly lists crab as a "Best Choice" seafood for pregnant women due to its low mercury content. The NHS caution applies only to raw or undercooked shellfish, not properly cooked crab. Guidance recommends eating cooked crab within standard seafood serving limits — not avoiding it entirely. A blanket avoidance recommendation is unsupported and could deprive mothers and babies of beneficial nutrients.