Combine lime juice, lemon juice, olive oil, and vinegar in a large bowl. Add cilantro, parsley, basil, salt, pepper, garlic, and crushed red pepper; mix thoroughly.
Add shrimp and toss to coat. Cover and refrigerate for 1 to 2 hours, tossing occasionally.
Preheat grill for medium-high heat.
Place shrimp in a grill basket. Grill shrimp until pink on the outside and opaque in the center, 5 to 6 minutes. Stirring regularly during cooking.