Short answer: Traditional Jain practice recommends avoiding seaweed.

Why:

• Ahimsa: Seaweed/algae grow in water that contains countless tiny living beings. Harvesting, washing, and processing can involve significant microscopic himsa.
• Sādhāraṇa vanaspati concern: Many teachers group algae/sea‑plants with categories avoided because they are associated with innumerable lives residing together.
• Contamination risk: Packaged seaweed is often flavored with fish/seafood extracts (e.g., bonito), or processed on the same lines as non‑vegetarian items.

If someone still chooses a lenient view (not the traditional ideal), at minimum they should ensure:

• Plain, vegetarian‑certified seaweed only (no fish/seafood/animal additives).
• Thoroughly cleaned and sun‑dried; consume fresh (daytime), not stored soaked/overnight.
• Avoid during Paryushan, Ayambil/Upvaas, and other vows emphasizing stricter ahiṁsā.

Both Śvetāmbara and Digambara household codes emphasize minimizing himsa; most observant Jains therefore refrain from seaweed.