Once the dragon cult was destroyed they claimed the empty Reach. The land's likely been theirs for ages, they have more right to it then the Nords. They're considered savages because they stay true to the old gods and the old ways which is hypocritical of Nords as they're going through similar treatment from the Thalmor who consider them savages.
The Reach is theirs and the Nords should respect it, they would have an ally of many tribes at their side in the fight against the Empire/Dominion.