I would imagine rinsing it would be a good idea, salt is no good for the plants.

No, rinsing it is not worthwhile. It's a waste of your time, and more importantly, it's a waste of water.

The amount of salt on seaweed is negligible for soil systems and compost systems. If you're adding so much seaweed that salt becomes a problem, then your soil system or compost system isn't going to be well balanced enough anyways to be successful.

Salt is no good for plants but with enough organic matter in a system other than seaweed you will be fine. What I do is usually add seaweed but in small layers at a time, separated with other organic material like leaves/grass/etc. Space it out and don't go overboard. You'll be fine. Don't waste precious water and don't waste your time.

Thanks for the info!
I was also worried that the chlorine in tap water would wreck some of the good stuff in the sea weed, anyway. Good to know rinsing isn't necessary as long as I don't use too much of it.

Rinsing seaweed is a waste, even if you have plenty of water.

I can't imagine chlorine causing a problem, People have been watering gardens with chlorinated water (and drinking it) for a long time with no apparent problems.

If you have good soil biology & organic matter going in your soil, all of this will counter any effects of chlorine or salt