Many like to compare Merida and Astrid to one another, especially in matters of Hiccup. They are violent, ill-tempered, handy with weapons and yet are the first to charge into a fight on behalf of their homestead.
The notion of the two being friends is unlikely enough. The history of the Kingdom of DunBroch dictated war with Vikings (as well as Romans and other Northerners), and Berk would naturally be on the list of Viking tribes that would have fought against them, either out of desperation from resources or natural viking ferocity. Astrid is incredibly patriotic on behalf of Berk and her tribe, and would be the first to throw her axe at the nearest highlander should any appear. Merida's temper and violent streak would cause her to fight back, either on the rebound or obligation to her kingdom. After working with each other, the two would learn to tolerate each other, become allies, then friends and (possibly) in a relationship.