On Nov. 30, the Supreme Court will consider whether to hear the case. On the same day, the justices will consider whether to hear two related cases, on whether Title VII bars discrimination based on sexual orientation. If the court agrees to hear any of the three cases, a relatively sleepy term will have gained its first blockbuster case.

The Trump administration filed a curious brief in Ms. Stephens’s case, one that said two seemingly contradictory things. The appeals court had gotten things badly wrong on legal issues that were “recurring and important,” Solicitor General Noel J. Francisco told the justices. The ruling, he added, was “inconsistent with decisions of other circuits.”

Those are precisely the things you say when you want to persuade the Supreme Court to hear a case. But Mr. Francisco went on to urge the court to deny review in the funeral home’s appeal and instead hear one of the cases on whether Title VII bars discrimination based on what he called “another non-biological-sex attribute — an individual’s sexual orientation.”

It is true that the appeals courts are more deeply divided on the question of whether Title VII covers discrimination against gay men and lesbians, with recent decisions from the Second Circuit, in New York, and the Seventh Circuit, in Chicago, ruling that it does. It could make sense to decide that question first, and to defer a decision in Ms. Stephens’s case in the meantime.

But Mr. Francisco went further, urging the Supreme Court to turn down the funeral home’s appeal even if the court declined to hear the two sexual-orientation cases. That has court watchers puzzled.

Mr. Francisco’s brief was nominally on behalf of the Equal Employment Opportunity Commission, which had charged the funeral home with employment discrimination and had prevailed in the lower courts. But his legal arguments were at odds with the views the commission had taken in the case.

Mr. Francisco’s brief abandoned the position that had been pressed by the commission in the Sixth Circuit and instead lent support to the funeral home. But in urging the Supreme Court to deny review, the commission remained formally aligned with Ms. Stephens, and the case is still known as R. G. & G. R. Harris Funeral Homes v. Equal Employment Opportunity Commission, No. 18-107.