What fruits, vegetables, raw meats, or spices are naturally blue?
Butterfly pea flowers, corn flower, chicory flowers, blue mallow flower and blue lotus all have blue flowers and the petals are used to make tea, in salads, or to spice foods (for the color).

Black goji berries are also supposed to make a blue tea, so probably have a blue juice.  If blueberries' purple juice disqualifies them, blue juice should qualify the goji berries even if they look very dark when whole.

Blue corn is also an option, as payton B mention - there are many varieties including hopi blue, aztec black (grinds to blue meal, so blue inside), santo domingo, lenape, or my favorite (and very visibly blue) baby blue jade corn.

There's also assorted odds and ends like blue sausage fruit or succotash bean, prickly caterpillar bean, fruit of the bilberry cactus, a blue kale, a blue-green tomato (the blue-reds tend to look black, but they're called blue), couple other blue tomatoes, blue potatoes, the blue carrot Sobachatina mentioned - some heirlooms can get oddly colored, it's fun.

Some of these do tend towards the purplish, but in every case either the inside is blue, the juice or pulp is blue, or there are pictures of truly blue examples as well as purplish ones (probably depending on pH of the soil).

There's also a double handful of blue flowers and berries that are ornamental, but not eaten, and again as much of purpleish ones that have some really blue pigment (in patches or along edges).