He was a descendant of David, who was a descendant of Judah, which genealogically would make him a Jew, if “Jew” refers to “descendants of Judah, and presently more generally of the other tribes as well”.

For a long time following his ministry, his followers were considered a sect of Judaism (or whatever it may have been called at the time). They were originally referred to as “followers of The Way”.

Jesus often went to the synagogues, attended the feasts, and followed the written Torah that was given to Moses. The rabbis that found him to not be practicing Torah were referring to “traditions” or the practices of the oral Torah and rulings. He chastised them for making the requirements of being observant too heavy to keep.