I was always suspicious that "Christian Science" didn't necessarily mean Christian.
This explains a lot -
CHRISTIAN SCIENCE CHURCH, a Christian sect, organized in 1879 by Mrs. Mary Baker Eddy. It is maintained that Christian Science attracted thousands of American Jews, particularly Jewesses, seeking health and peace of mind through its religio-therapeutics. Because Christian Scientists do not undergo baptism upon joining the church, some Jews asserted that membership entailed no apostasy from Judaism. This situation of Jews openly dividing their religious allegiance between Christian Science and Judaism prompted the Central Conference of American Rabbis (Reform) to warn in 1912 that "adhesion to the one means rejection of the other." Other Jewish reactions to the drift of Jews to Christian Science included the publication of Rabbi Alfred Moses' Jewish Science (1916) and the organization in 1923 in New York City of the Society for Jewish Science by Rabbi Morris Lichtenstein. His system of faith healing employed techniques and rhetoric borrowed from Christian Science, Judaism, and popular psychology, but neither Lichtenstein's nor other "Jewish Science" groups had a lasting influence on American Jewry. After Lichtenstein's death in 1938, leadership of the Society passed to his widow Tehillah Lichtenstein, the first woman to occupy a pulpit and assume quasi-rabbinical leadership in an American congregation. She held this position for over 30 years.
https://www.jewishvirtuallibrary.org/christian-science-church