This is a fairly well-trodden theory (although obviously controversial among Christians) in studies of early Christianity (see, for example, the Vatican conference on Jesus and the Pharisees).
The question is less “Would Jesus (if he existed as portrayed in the NT) have considered himself a Pharisee?” (impossible to know) than “Would your average first-century Jew have considered him a Pharisee?”
As for that, here’s what we know about the Pharisees:
- Were attempting to create flexible, livable interpretations of Jewish law to adapt to the changing circumstances of the Jewish people
- Were decentering Jewish practice from the Temple into the home or community centers (synagogues)
- Usually had circles of students
- Didn’t have an infrastructure for getting paid for teaching, so they generally either had a second profession or were supported by patrons, which often involved traveling
- Taught and learned through debate—agreeing with other Pharisees on most issues wasn’t necessary to be one, and they disagreed with each other on all kinds of stuff while still having a fairly unified general ethos on the need to adapt
- Weren’t Roman collaborators (Sadducees) or calling for immediate revolution (Zealots) but were anti-Roman
- Weren’t isolationist like the Essenes/Therapeutae—remained closely involved with their communities
- Engaged with gentile “God-fearers” who believed in the God of Israel and some of the tenets of Judaism without converting to Judaism
The NT frames exchanges that would be well within the norms for Pharisaic debate as inexplicably hostile. Jesus disagreed with them on divorce, therefore they plotted to kill him!!!
Weird, because they disagreed with each other on L I T E R A L L Y E V E R Y T H I N G and weren’t trying to kill each other over it.
The Pharisees approaching Jesus to debate with him, if you look at the substance of their encounters and ignore the narrative insisting that they had Nefarious Intentions!!!!, is how they engaged with each other. They didn’t spend their time debating Sadducees. Debate was an intracommunity activity, not something they wasted effort on doing with their enemies.
Jesus has dinner with Shimon the Pharisee, which was fairly normal practice for traveling rabbis who guest-preached at a synagogue. They’d stay with a prominent community member while they were in town.
The Pharisees also warn Jesus that Herod is looking for him (also a normal thing to do for someone you see as a member of your community, even if you disagree with him on some things).
Early Christianity was at pains to prove it wasn’t just another Jewish movement, which meant attacking the Jewish movement it arose out of and was closest to.