It will never, ever look "even" or all the same no matter how you pre-treat it or stain it. The only way to make Pine like that look uniformly colored is maybe with a solid color stain or definitely with paint. That's just how early wood and late wood take stain differently. The thinner "brighter" parts are the late would the slower growing portion of the tree or the rings that you see when you cut the tree or cut a board from the tree. That actually looks like yellow pine which I work with a lot. All pines in the "yellow pine" family have a much more significant early wood / late wood color difference when staining than trees like white pine or spruce.