Raspberries are usually NOT blue. In fact, the color blue is fairly uncommon amongst fruits. Why exactly, then would sweets makers specify the flavor as blue raspberry? It's rare to see 'green' and 'purple' grape flavors, for example.
It all started with ice pops. Very popular in the 60’s and 70’s, ice pops like Otter Pops came in a variety of colors and flavors. The sheer number of flavors that were red colored fruits had started to confuse the ice pop makers and the customers. Cherry, strawberry, raspberry, and watermelon were all red, and it was difficult to distinguish them.
At first, using different shades of red was no problem, until one of the dyes used was deemed a carcinogen by the FDA and was banned. So how did the makers of ice pops respond? They had plentiful access to blue dye, but had no flavors that needed it.
They started to introduce the flavor of the Whitebark Raspberry (or blue raspberry) with the blue food coloring, and even though the color of the berry is completely different from the color of the dye, the problem with the dyes was solved.