They are very effective towards protecting the thyroid gland, but only the
thyroid gland.

To say they are nonsense altogether is, well, nonsense.

Protecting my thyroid gland, and only my thyroid gland, doesn't seem like a
particularly successful or efficient means of shielding myself against
everything else high radiation can do to the entire body.
Just because the Soviets distributed nukepills to its citizenry doesn't mean
there is any good reason for having done so.
But the real point is that these things are being sold to play on fears of an
ignorant public, and there is very little science behind it to rationalize the
cost or usefulness of them.
It is, in fact, nonsense.
Linus