You don't really have light sources which are all that broad spectrum- each is associated with a particular temperature dictated by the technology. The technology of holograms remains one of light projection, and blue light is clearly the color associated with the illuminator associated with that technology.
Taking this a little further, given that there are other colors besides blue, The blue light is acting as a sort of carrier wave- it illuminates dust particles in the air to see the image, creating the "screen". Other colors can be projected on to the illuminated area which give contrast, but it is the blue light which is the workhorse and will bleed through.
In instances where non-blue tints holograms are present, they may be in special setups. Examples can include: pre-rendered CGI creations broadcast in a specialty projection area. I don't believe we have ever seen live broadcast which was not blue (which would seem to hint that it requires a fair amount of computational horsepower to overcome). But what about Leia's message? Well, it was the equivalent of recorded in a rush in a prison from a hand-held camcorder. Works well enough for the purpose but you wouldn't expect anything Spielburgian.