Prepare the gluten free red velvet cake according to the package directions in a 9 by 13 inch baking pan. Bake until a toothpick inserted in the center comes out clean. Let the cake cool completely in the pan, about 1 hour.
Once fully cooled, use your hands to crumble the entire cake into fine crumbs in a large bowl. There should be no large chunks remaining. Add the cream cheese frosting and mix thoroughly until the crumbs hold together when pressed.
The mixture should feel like wet sand that sticks together easily.
Using a small cookie scoop or tablespoon measure, scoop out portions of the mixture and roll them into smooth, tight balls about 1 1/4 inches in diameter. Place them on a parchment-lined baking sheet. You should get about 24 cake pops. Refrigerate for at least 30 minutes until firm.
Melt the white chocolate chips and coconut oil together in a microwave-safe bowl, heating in 30-second intervals and stirring between each until completely smooth.
Dip the tip of each lollipop stick about half an inch into the melted white chocolate, then insert it into a cake ball, pushing halfway in. This acts as glue to hold the stick in place. Repeat with all the cake balls and refrigerate for 10 minutes to set.
One at a time, dip each cake pop into the melted white chocolate, tilting the bowl and turning the pop to coat it evenly. Let the excess drip off, then immediately add red sprinkles while the chocolate is still wet.
Stand the finished cake pops upright in a styrofoam block or place them on parchment paper. Let the coating set completely at room temperature for about 20 minutes.