There is a spectrum of scholarly opinion.

 ON THE RIGHT

There have been distinguished scholars who believe that Jesus’ position was within the Orthodox Jewish range. (see scholarship of Hyam Maccoby, Joseph Klausner, David Flusser).

Some believe that Jesus shifted “rightward” over the years from (classic) Orthodox to Nazirite (Orthodox) at the time of his killing. Note that Nazirite is a highly ascetic mode of Orthodox, and more to the “right” than (classic) Orthodox. His younger brother, James the Just was Nazirite.

ON THE LEFT

Others believe that he was to the ‘left’ of Orthodox. These scholars sometimes employ the term “common Judaism” (see scholarly works of E.P. Sanders) to describe his practice. By that,  they mean sort-of Traditional, which itself is a pretty wide term. Here they mean the Judaism of the “average (or random) Jew” of the First Century: Festivals, Temple, Kashrut. Of course, that is not the observance of the ‘average (or random) Jew of the 21st Century, which is typically far to the ‘left’ of that Festivals-Kashruth cluster.

Note, as well, that Jesus may indeed have shifted ground within Judaism over the years.” The scholarship on the subject (“the real Jesus”) itself shifts subtly over-the-years.