In a small skillet, heat 2 tablespoons oil over medium heat. Add the garlic and ginger and cook over low heat, stirring frequently, for 5 minutes. Add the curry powder and crushed red pepper; season with salt and black pepper and cook, stirring, for 1 minute. Transfer half the garlic-spice mixture to a medium bowl, leaving the remaining mixture in the skillet.
Add the shrimp, cilantro, 1 1/2 teaspoons vinegar and the remaining 1 tablespoon oil to the mixture in the bowl. Season with salt and black pepper and toss to combine. Cover with plastic wrap and refrigerate for 30 minutes.
In the skillet with the remaining garlic-spice mixture, add the cranberry sauce and the remaining 2 teaspoons vinegar and cook over low heat, stirring, for 5 minutes. Season with salt and black pepper and transfer the cranberry chutney to a serving bowl.
Heat a grill pan over medium-high heat. Grill the shrimp until opaque and just cooked through, 2 to 3 minutes on each side. Serve with the chutney.