Well, I'm sorry but if you want a phone with an AMOLED screen it's just something you'll have to live with. I find that because I'm actually using my screen, I'm normally looking at it head-on so I don't see the blue shift.
But, there are many positives and negatives for both AMOLED and LCD screens that there is a trade-off when choosing either.
-AMOLED Blacks are actually black - LCD Blacks are slightly lighter because there's a backlight and the crystals cannot block the light completely
-Outdoor visibility suffers a bit but it isn't great with any non-e-ink screen.
-AMOLED screens have more vibrant colors, while LCD ones can often have a white pallor with colors looking washed out
-AMOLED screens suffer blue-shift when increasing viewing angles but the screen remains highly clear (although it is much less severe in modern displays) LCD screens turn gray and distort when looked at from an angle.
-AMOLED pixels require no power to display black colors, so the screen can produce a lot of power savings over LCD ones when displaying many dark screens. LCD's use a backlight which remains constant meaning the pixels work harder to block light. Dark screens draw more power on LCD.
-AMOLED allows for features such as Moto X's Active Display because each pixel provides its own light so only the pixels being used draw power.
In all, there are drawbacks to using any type of screen, so you just have to decide which ones you want to live with. Personally the blue shift on my Moto X is very slight so I'm more than happy to live with it in exchange for the benefits AMOLED gives me.