Wie wäre es damit?

Also, entweder "radical political statements" oder "politically radical statements"!

No, not entweder/oder. They're two different meanings

"Radical political statements" are political statements that are radical in nature.

"Politically radical statements" are radical statements only in a political sense.

George Bush decided to become a Democrat. That's politically radical (to the Republicans), but it's not a radical statement per se.

The translation of the German can, therefore, only be "politically radical statement."