Recused, it turns out, if the brother is Justice Stephen Breyer and the other brother is Judge Charles Breyer. As Tony Mauro (Legal Times) reports, “Breyer makes it a practice to recuse in cases that were handled by his brother Charles, a federal trial judge in the Northern District of California.” My quick search for (charles +3 breyer) through the Westlaw SCT database supports this — in all three cases found by the search (Olympic Airways v. Husain, Department of Housing and Urban Development v. Rucker, and U.S. v. Oakland Cannabis Buyers’ Co-op.), Judge Breyer was the judge below and Justice Breyer recused himself.
This turns out to be important in the case involving the jail strip search / visual body cavity search policy, Bull v. City & County of San Francisco. Judge Breyer was the trial judge in that case, so presumably Justice Breyer will recuse himself. So if plaintiffs petition for certiorari, they need five votes without Justice Breyer’s vote (since a 4-4 vote affirms the decision below).
To get to those five votes, plaintiffs would have to get at least two votes from the Court’s conservative wing. I doubt they will get those two votes. They might not even get some of the liberal votes — even Justice Breyer wouldn’t be a sure vote for the plaintiffs. Still, without Justice Breyer, the plaintiffs would have to persuade not just the moderate conservative Justice Kennedy, but also one of the more solid conservatives (Chief Justice Roberts and Justices Scalia, Thomas, and Alito). Pretty unlikely, it seems to me.
So plaintiffs’ lawyers face an especially tough choice when deciding whether to petition for certiorari. The lawyers, given the nature of this case, are interested in jail inmates’ Fourth Amendment rights more broadly, and not just in getting a victory for their clients in this particular litigation. (I suspect the clients have a similar view.) They must thus be worried that if five votes come out against them, the Ninth Circuit precedent would become nationwide, and diminish the Fourth Amendment rights of jail inmates throughout the country. That’s the cost of a cert petition. And the possible benefit of a cert petition seems especially improbable, given Justice Breyer’s likely recusal. So Judge Breyer’s role in this case might lead the plaintiffs’ lawyers to avoid petitioning for Supreme Court review in this case.
UPDATE: On the other hand, here’s a different analysis from commenter tvk:
[If plaintiffs] lose 4–4, with Kennedy joining the liberals and where Breyer’s vote might have made it a win … from a long-term strategic standpoint, [that's] not a bad result. The equally divided court creates no precedent; the Ninth Circuit opinion stays on the books but is heavily undermined. Everyone will predict that in the next case, Breyer will jump onboard with Kennedy and the liberals, so you can predict that other courts of appeals will jump in front of the bandwagon. The individual petitioner loses, but that was never quite the point anyway, as you point out.
FURTHER UPDATE: I forgot to mention that the Court sometimes considers whether a Justice will be recused when deciding whether to grant a case. And I would think this would be especially likely if the case seems likely to split 4-4 — who wants to do the work required to prepare for the case (and make the lawyers do all that work), only to have the case affirmed by an equally divided court? So that, coupled with the greater difficulty of getting 4 votes to grant, coupled with the possibility that the liberal Justices who are deciding whether to grant will probably doubt that they’ll get 5 votes to reverse, decreases the probability of cert. The probability is still substantial, given the 6-5 vote below, and the circuit split. But it’s less than it would have been had the trial judge been someone besides Justice Breyer’s brother.