Short answer, no.
The basis for the article's question comes from last week's Town of Greece oral argument (pp. 18-19).
Justice Scalia asked counsel: "[W]hat is the equivalent of prayer for somebody who is not religious?"
After a brief colloquy between Scalia and counsel, Breyer said: "Perhaps he's asking me that question and I can answer it later." (Counsel's time was about to expire.)
Some people are reading that as Breyer admitting he is an atheist.
A question for Breyer (if that's what it was) does not necessarily mean a question about Breyer or his beliefs. As, in fairness, the HuffPost article points out, Breyer could have been talking about his ability to at least restate other people's "not religious" viewpoints. In any case, "not religious" does not always equal atheist.
Breyer, who is Jewish, is a regular at the Red Mass, a Catholic service held before the opening of each new Supreme Court term. He has attended the last seven, including one just a few weeks ago.
His daughter Chloe, an Episcopal priest, writes in her book, The Close: A Young Woman's First Year at Seminary (2000), that "Church-based activity was more the exception than the rule as I was growing up" (p. 156). But the exceptions are telling. Breyer attended, hosted, and encouraged participation in religious events.
I grew up in an interfaith, academic household, the daughter of an American Jewish father and an English Anglican mother, and I was baptized into the Church of England as a young child. During the few years my family and I attended an Episcopal church in Cambridge, each of us had different reasons for going. My mother liked singing the traditional Anglican hymns she had grown up hearing in England. My father respected the old Irish American rector and thought my brother, sister, and I should have some exposure to organized religion—even if it wasn't his own Jewish faith. We came to know more about our Jewish heritage when my father began holding annual Passover Seders and attending Rosh Hashanah and Yom Kippur services (Introduction, xiii).One end note: Justices, like all judicial and executive officers, need to take an oath to support the Constitution; however, "no religious Test shall ever be required as a Qualification to any Office or public Trust under the United States." Art. VI, para. 3.
Since the Constitution says justices' religion shouldn't be an issue, why bring it up? (But, of course, we do.)