All cameras can take photos under blue lighting properly. It's the white balance that needs to be set properly. Unless you get to grips with setting the white balance to something appropriate (even a daylight preset will be decent, far better than "auto") then you're going to have this problem with any camera, regardless of cost.
That's quite a lot for a compact camera, for that money you could get a small pro-sumer DSLR. Although then comes costs with additional lenses etc. Compact bridge cameras costing half that have similar, only marginally lesser specs.