Horseshit.
Jesus' crime in those stories was to proclaim himself God. Caesar was, in fact, God. Declaring oneself to be above Caesar was a serious crime, punishable by death.
The gospels were supposedly written by men imprisoned by various tribes throughout the region, that were controlled by pharisees (whom did not exist as a power structure at the supposed time that Christ actually lived--meaning, they would not have been around to actually persecute and prosecute Christ).
The gospels were a polemic, written by political prisoners, against the established order of their time.
The charge as recorded was, "Jesus of Nazareth, King of the Jews."
If he claimed to be the Messiah he would have been claiming kingship ("savior" only being a secondary concept associated with the anticipated role of the Messiah). "Messiah" had become a generalized term for the anticipated descendant of David who would revive the kingdom to one degree or another depending on the sect. Messiah (Heb. mashiach; Grk. christos) means to annoint (by pouring or smearing of oil). It was common in ancient Judaism to annoint kings and priests and Psalm 2 already conflates kingship with annointing.
The Gospels/Acts/Paul all ascribe to Jesus the proclaimed status of Messiah/Christ aka King. This lends support to the accused crime of claiming to be king.
Romans had no issue with other gods; but they did initiate the
Imperial Cult and expected homage (Jews typically exempt).
RE: Pharisees. Josephus, the Mishnah and Tosefta, and Acts/Gospels fail to support your position. Understanding that all sects lacked absolute power, the picture is more complex. The Herodians were the established civil authority (but under the Romans) and the High Priest (typically a Saducee) were in charge of cult affairs. But it is complex because there were many priests who were not Saducees. The Pharisees have enough public support that their practice regarding counting the Omer (for the festival of weeks) was the one carried out in the Temple; ponder that, the Saducees administered the Temple procession and yet had to conceed to the Pharisees due to their wide ranging support. Another dynamic was the Sanhedrin which would have been respected as an authority structure within Jewish culture; I have seen no dispute regarding the presence of Pharisees within this group.
On the other hand Hellenistic Jews exerted significant influence outside Israel (heck, even northern areas of Israel in the Galil were primarily gentile). While it is true the spiritual successors of the Pharisees (the Rabbis), post Yavneh exerted sizable influence throughout most Jewish sects this power was not near as sizable as claimed in the Diaspora pre-destruction.
So I would take issue on both sides of the Pharisee coin: they were extremely influentual in Jerusalem; not so much (politically) outside.
For what is is worth, while the recorded charge was sedition (king of the Jews; see the procession the week before upon his entry into the city) the interpreted motives by the Gospel authors vary: false prophet, conflict in existing teachings, threat to religious authorities, understood as threatening the Temple, claiming kingship, applying religious texts, like Daniel 7, that could be considered blasphemous, etc). This is why the recorded court case is all over the place--various parties took issues with different claims or supposed claims. Often missed by modern authors is the witnesses that he threatened the Temple--not a small accusation.
If the Gospels are to be trusted Jesus irritated all the major factions for different reasons. What isn't disputed is that a Jew could be drug before the Sanhedrin for claims of blasphemy, sedition, or threats to the Temple. All serious matters that any Jewish witnesses, not just the Pharisees, could bring before the Jewish court. There is no doubt the Pharisees existed (Hillel and Shammai say hi!) and a structure existed for them to bring forth accusations.