My ginger is blueish... is it safe?
Having just returned from Hawaii, I actually have a possible answer for you. There is a type of ginger that you can get there (though it's not all that common, far as I could tell) that's called blue ginger. It's just like regular ginger, only it has the blue layer inside as you describe. There was a guy selling it at a roadside fruit stand when we were there.

It should be absolutely safe to use.

edit: I found a link to somebody talking about it. Hawaiian Blue Ginger