Did Roman statutory law in the 1st century allow for crucifixion of non slaves?

There is no such thing as "Roman Statutory Law". The legal system in Rome was centered around magistrates, and their agents called lictors. Magistrates had imperium, which meant they had wide latitude to do whatever they wanted, especially in provinces like Judea.

As far as your professor's claim that crucifixion was limited to slaves, that was normally true until the time of the Judean revolt in 66-73 AD, when crucifixion was also used against the rebels. I know of no instance in Roman history where a Roman citizen was recorded as having been crucified in Rome.

During the Judean revolt many non-slaves were crucified. The population of provincial states like Judea were considered provinciales which was a type of citizenship, but not full citizenship. In the Roman empire there were many different classes of citizens. In any case, during the revolt non-slaves were crucified, so that would seem to contradict the professor's statement of fact.

As far as the professor's basic idea, it has some validity, even if it is incorrect in the details. In 30 AD, relations between the Romans and Judeans were relatively cordial and the Romans were mostly located in Caesarea, very far away from Jerusalem. The idea that a Roman prefect and soldiers would enter Jerusalem and crucify a local seems very unlikely given the political situation at the time. One of the few historical details known about Pontius Pilate is that he sent a Roman unit to Jerusalem and it caused a huge scandal because some of their banners had embroideries of the emperor's picture (Tiberius). Pictures of people are illegal under the Torah. Once this became known, Pilate immediately ordered those banners removed from the city out of respect for the local laws. It is common sense that if such a little thing was disallowed, holding a crucifixion would be unthinkable because the affront to the Torah for such a thing would be a thousand times worse than a mere picture.

As far as the idea of Jesus having been "deported", what is the evidence for this that the professor gives? Even if Jesus had not been crucified, that does not imply that he was "deported".

In the Aqueduct riots Pilate sent in the troops on a mob and many were slain - and it was explicitly said by Josephus that non-rioters were also killed. Pilate was hardly averse to treating potential unrest with severe force...and a claim to be King of the Jews is treason and a call for rebellion.

As far as I know, the Romans never practiced deportation as a punitive measure against provincials. Simply killing off an offender was the expedient and simple Roman way.

P.S. A citizen under trial could go into voluntary exile before the verdict was handed, to escape forfeiture of property but that was (a) under the Republic (b) applied in practice only to a handful of relatively prominent individuals (e.g. Verres or Rutilius Rufus) who were indicted for political reasons, whether guilty or not.

Jesus was not a Roman citizen. He was not one of the provinciales because he was not born in Roman province (Iudaea).

"The Closing of the Western Mind" by Charles Freeman, chapter 8, says he was born and lived almost entire life in Galilee, which was part of a "puppet state" ruled by a king (e.g., Herod Antipas). Jesus came to Iudaea between 29-33 CE, most probably in 30 CE.

"Crucifixion in the Mediterranean World" by J. G. Cook similarly asserts on page 216 Jesus was a peregrinus ("foreigner, one from abroad" but in practice a subject of Empire as opposed to barbari), and that there were in all 9 recorded names of crucified peregrini. For example he includes Theodotus rhetor. Also we know three names of crucified full Roman citizens: Valerius Soranus, Gavius of Consa, Gaius Silius.