Fuji X-E1 White Balance Concerns

I agree with the previous poster, each camera gives slightly different colours and indeed every colour 'mode' on each camera gives slightly different colour again.  When you get a new camera you need to fiddle until you are satisfied with the colour output.  Of course, there are times when no amount of fiddling is going to satisfy you and that is when you give in (I struggled with skintones out of the Nikon D7000 and gave up in the end).

I find the AWB of my (yes I have one!) Fuji X-E1 under artificial indoor light a pain but many cameras are the same there so I just manually adjust.  No issues yet at any other time though, my blue skies are generally blue.