Heat the oven to 200°. Line two baking sheets with parchment paper, then place lollipop sticks on each pan, spacing them evenly.
With a hand or stand mixer set on medium speed, whisk together egg whites, vanilla, cream of tartar, and salt. Once it's foamy, gradually add sugar and continue mixing until stiff peaks form, about 4 minutes. Evenly divide the meringue between two bowls.
Whisk red food coloring into one bowl and blue food coloring into the other. Transfer each to a ziplock bag with a corner snipped off or to a piping bag fitted with a large round tip (like an Ateco #9).
Pipe the meringue in a circular motion onto the sticks. Blend the swirls with a toothpick, using the tip to form small peaks.
Bake the meringues on the upper and lower-middle racks until firm and dry, about 1 hour 45 minutes. Let them cool completely before removing them.