See if his SWAMI recommends the bladderwrack supplement or not. Sometimes the supplements are OK even if the individual foods are not, as the supplements may be different varieties of herb than the typical foods, and/or there may be a harmonic healing effect with other ingredients in the formula. I remember asking DPN about proberry syrup, since it contains pear juice, a "black dot" on my SWAMI. They said it was fine.
I'd stop using kombu in shared soups, but find a way to add to just your portion. I buy granulated kelp which I can easily add to my bowl of soup, or a smoothie, or an omelette.