Line a baking sheet with parchment paper. Set the pretzel rods aside while you prepare the coating.
Place the white chocolate chips and coconut oil in a microwave-safe bowl. Heat in 20-second bursts, stirring between each, until fully melted and smooth.
Dip both ends of each pretzel rod into the melted white chocolate, leaving the center uncovered. Place the coated rods on the prepared baking sheet and let them set at room temperature.
In a small saucepan over medium-low heat, combine the cheddar cheese, cream cheese, milk, garlic powder, and paprika. Stir steadily until the cheeses melt and the mixture becomes smooth and creamy.
Transfer the cheese dip to a serving bowl. Arrange the coated pretzel rods around the bowl for dipping.