Combine strawberries, half of dates, and ¼ cup plant milk in a blender; puree until smooth. Pour into ice pop molds and place in the freezer until set, at least 20 minutes. (Make sure each layer freezes until set so it won’t bleed into the surrounding.)
Wash blender thoroughly. Combine sliced bananas with ¼ cup plant milk in blender; puree until smooth. Pour this layer over strawberry mixture and return to freezer until set, at least 20 minutes. At this point, insert craft sticks into center of each mold (the stick should stand on its own).
Wash blender thoroughly. Combine blueberries with remaining dates and plant milk in blender; puree until smooth. Pour over frozen banana mixture and return to freezer for at least 1 hour.
Remove ice pops from freezer and let stand for a few minutes until they easily release from molds. If needed, place molds briefly in a container of warm water to loosen from molds. Serve immediately.