There is a lot of noise out there about the Seattle case. There is a rather personal left right split on the court, but none of it matters because Kennedy's opinion is the weakest link in the majority, and his conclusions are rather narrow.
In today's school-assignment cases, Justice Kennedy's opinion controls, as he was the 5th vote to overturn the Seattle and Louisville school assignment plans, and the reasoning in his concurrence is narrower than that of the Chief's plurality opinion.
As to the Seattle plan, the key paragraph in Kennedy's concurrence, it seems to me, is this one:
"In the Seattle case, the school district has gone further in describing the methods and criteria used to determine assignment decisions based on individual racial classifications, but it has nevertheless failed to explain why, in a district composed of a diversity of
races, with only a minority of the students classified as “white,” it has employed the crude racial categories of “white” and “non-white” as the basis for its assignment decisions. Far from being narrowly tailored, this system threatens to defeat its own ends, has provided no convincing explanation for its design."