Position a rack in the upper third of the oven and heat the oven to 350°F.
Briskly simmer the cider in a small saucepan over medium heat until reduced to 1/2 cup, about 5 minutes. Add the raisins and set aside to cool.
Combine the apple, grapes, parsley, and scallion in a medium bowl. Add the cooled cider mixture and toss. Season to taste with salt and pepper.
Arrange the bread slices on a rimmed baking sheet and brush the tops with olive oil. Bake until crisp and pale golden, about 10 minutes.
In a medium bowl, toss the collard greens with the 1 Tbs. olive oil, the vinegar, and salt and pepper to taste.
Spread the cheese on the crostini. Top with the greens, pressing them gently so they’ll stick to the cheese. Using a slotted spoon, top with the relish. Serve immediately.