The Supreme Court has decided Rivera v. Illinois. Justice Ginsburg wrote for a unanimous court.
This Court has “long recognized” that “peremptory challenges are not of federal constitutional dimension.” United States v. Martinez-Salazar, 528 U. S. 304, 311 (2000). States may withhold peremptory challenges “altogether without impairing the constitutional guarantee of an impartial jury and a fair trial.” Georgia v. McCollum, 505 U. S. 42, 57 (1992).
The point for military practitioners is the appellate courts — both the state and U.S. Supreme Court — finding that there was no evidence of a prima facie case of discrimination and that the trial judge erred even in asking counsel for an explanation of the challenge. The state supreme court resolved the issue on lack of prejudice, and the U.S. Supreme Court resolved on the basis that there is no federal constitutional right to peremptory challenges. Thus it would appear that a trial counsel's mere request for an explanation must itself be denied, unless the trial counsel sets out reasons why they think there has been a discriminatory challenge and the military judge agrees that a prima facie issue is raised. A mere, "they've challenged a woman" doesn't cut it either. There was no challenge for actual or implied bias in Rivera. On my reading of the facts there could have been an implied bias challenge based on the voir dire of the challenged juror. I'm of the view that once there's been a challenge for implied bias, with the reasons stated, there are not likely to be successful challenges to a peremptory challenge. This is different from the issue of how the initial error of failing to excuse the member on an implied bias challenge should be dealt with by the appellate courts (see below). The decision in United States v. Martinez-Salazar, 528 U. S. 304 (2000)(use of peremptory challenge to cure a denied challenge for cause under federal rule), seems to support that result. Justice Ginsburg also wrote the opinion in Martinez-Salazar, where the she wrote that:
federal criminal defendant’s choice of whom to challenge peremptorily.
Under the Equal Protection Clause, a defendant may not exercise a
peremptory challenge to remove a potential juror solely on the basis of
the juror’s gender, ethnic origin, or race. See, e.g., J. E. B. v. Alabama ex rel. T. B., 511 U.S. 127 (1994) (gender); Hernandez v. New York, 500 U.S. 352 (1991) (ethnic origin); Batson v. Kentucky, 476 U.S. 79 (1986) (race).
United States v. Martinez-Salazar, 528 U. S. at 315 (emphasis added).
Note, that under current rules, military counsel are required to use the peremptory challenge to preserve a denied challenge for cause; the result argued for but denied to the government in Martinez-Salazar. See R.C.M. 912(f)(4). You might be interested in CAAFLog's view of the 2005 Manual change. CAAFLog points out that the Manual was changed to "conform" to federal practice," but that interestingly the Manual was not changed to add additional peremptories as required in federal practice. So the Manual was conformed to take something away for the accused, but not add. Another example for cynics of how the DoD "changes" and cherry-picks the rules to suits them.