At 35, he is part sports mogul, part holy man. With some 15 years as a basketball star, Mr. Stoudemire has stepped out as an entrepreneur, dipping into the art and fashion worlds, opening a winery and publishing a series of books. He is also taking what he frequently calls a “spiritual journey” into the Bible, Israel and Judaism. It’s a turn that has fascinated and confounded some observers.

A museum employee hurried behind Mr. Stoudemire to point out pieces of interest, sprinkling her sentences with Yiddish and craning to make eye contact. But Mr. Stoudemire seemed at ease among the cases of Judaica, explaining items to two friends and his wife, Alexis Welch, who accompanied him.

Walking past a collection of ritual rams’ horns from the 18th century, one friend asked, “Have you ever played one, Amar’e?” Mr. Stoudemire nodded. “It takes practice to find the right channel,” he said, “but it’s a profound sound.”

Mr. Stoudemire was raised in a churchgoing home but has long felt more of an affinity for the ancient Hebrews of the Bible than for modern-day Christians. He has made a dozen pilgrimages to Israel, the first in 2010 (and would one day like to move there), and studies Torah daily, peppering his social media feed with Hebrew words and phrases. He also uses a biblical moniker, Yehosaphat.

This name was splashed in big white letters on the black leather jacket he wore to the museum. Two necklaces glittered on his chest; one, a Hebrew menorah, the other, a Jesus medallion.