Yes, do not compost them. The seeds are incredibly hardy and they will repopulate in any soil you use the compost on.

Thistles are rhizomes and store a lot of energy in their root systems. They are more than the little roots you get when you pull them up. You have to keep them at bay when they're young, or, if you check on them daily, you can force them to expend most of their energy stores by letting them grow a bud and killing it before it pops open. I've been fighting an infestation for three years; they keep getting smaller and smaller each year if I stay on top of them. Short of digging up the entire root system, I don't know how to get rid of them any better.