The name Blue Rat is lifted from a fictional East European beverage that features in the first series of 15 Storeys High. If this is new to you, you may find the following excerpted video instructive.
In addition to the rather esoteric primer on the origin of Blue Rat offered above, it should be noted that the colour blue is not intended as symbolic in any way (politically, religiously, or otherwise). It merely happens to be the colour of the rat. The colour of the rat is also not down to genetic novelty, as might have otherwise been infered from this article regarding blue rats in general. No, Blue Rat is a-causally blue. That is to say, for no other reason than that blue happens to be his colour. There is no direct causal connection between Blue Rat and any item or concept preceding him associated with the blue colour. That should now be clear.
If you’re still confused and need further clarification, this video should do the trick: