A federal judge cleared the way on Tuesday for California’s new law banning gay “conversion therapies” for minors, one day after another federal judge, in a separate decision, called the ban an unconstitutional infringement on speech. Because Monday’s ruling by Judge William B. Shubb, of Federal District Court in Sacramento, was applicable only to three plaintiffs in the suit before him — two practicing therapists and a former patient — it appeared the state’s ban would take effect on Jan. 1 as planned. But the contradictory rulings, and the prospect of appeals from both sides of the issue, suggested that the law, the first of its kind, could be embroiled in the courts in the months ahead. The ban had been hailed by gay rights advocates and mainstream mental health groups that call therapies that try to alter the sexual orientation of youths potentially damaging. Judge Shubb’s ruling sharply challenged the law, and left little doubt that in his court, as he put it, “the plaintiffs are likely to succeed” with their argument that the law violates free speech. But on Tuesday, Judge Kimberly J. Mueller, in another federal court in Sacramento, held that the plaintiffs in her case — two former patients and their parents, who also challenged the law — were unlikely to prevail and refused to prevent the law from taking effect.