Some don't compost any weeds!

My compost bin would be empty if that were the case for me though!

Perennials like dandelion can be dried in the sun before composting, along with thistle roots.
I wouldn't compost mares tail or bindweed though, dried out or not.
Just as an aside I had heard about drowning bindweed in a water barrel and using it as a feed so I stuffed a handful into a water barrel. Imagine my dismay when a fortnight later I looked in the water barrel and I had bindweed climbing up the fence next to it with roots at every node, floating in the barrel!

PS I should add that its common sense NOT to compost weeds once they have seeded!