I've read that after kicking his pregnant wife Poppaea to death, Nero castrated a boy who resembled her and took him as his wife. It seems to me that it must have been relatively accepted, as Nymphidius Sabinus then took Sporus as a wife after Nero's suicide. Further reading shows that Sporus was addressed as "Mistress" and occasionally "Empress", but was this sort of sexual identity considered taboo in ancient Rome? Would people have been aware of Sporus's situation?
Would it have been viewed as another sign of Nero's power? Or did people not understand the circumstances and assume that Sporus was born female? On that note, was Sporus what we consider today to be transgender, or was this a situation that he was forced into in conflict with his own accord?
Furthermore, I've read that Nero also took a husband, Pythagoras. What was his reason for doing this?
Forewarning that I’m not a specialist on gender roles or homosexuality in Ancient Rome and my knowledge comes more from broader studies of Roman society in the first century AD and the reign of Nero. Hopefully if I make any mistakes someone more specialised on this exact subject can clarify/correct me below.
So to answer your last question about what gender Sporus would be considered: the Romans did not have the same distinctions such as “transgender” that we have today so it would be difficult to make a direct equivalent comparison. Instead it is assumed that Sporus belongs to a subset known in Rome as a “puer delicatus” - a “delicate boy” who were known for their youthful and effeminate looks and generally groomed for sexual favours by their master. A more well known term might be “catamite”. Specifically these were slave boys and not free Roman men (puer, Latin for boy, is to be distinguished with vir, Latin for man - which a slave would not be called regardless of his age).
As to how the Romans viewed Sporus we can look at this within the broader context of puer delicatus within Roman society, and then look at the circumstances of Sporus in particular.
Puer delicati were relatively common in Ancient Rome among the elite. For example the emperor Augustus was known to have one called Sarmentus. In Suetonius’ account of Augustus’ life he tells us that Mark Antony made scandalous accusations against Augustus in an attempt to tarnish his reputation: these were mainly that he had sold his body to leading men (including Julius Caesar) - but crucially there is no mention of his Puer Delicati. In fact Suetonius instead tells us that Augustus was a womaniser who enjoyed deflowering virgins. This overlooking of Sarmentus links to how the Romans viewed homosexual relationships and sex. For the Romans what was more important was who was submissive/dominant in the relationship: having sex with a male slave is not scandalous as they are clearly submissive to their master, on the other hand prostituting yourself or sleeping with freeborn men is more scandalous because socially they would be considered equals.
In the Satyricon by Petronius, a fictional “novel” (in a loose sense of the word), a decadent and extravagant freedman called Trimalchio, known for his vulgarity, makes mention of his frequent sexual relations with one of his slaves, a puer delicati, who we are told was also frequented by Trimalchio’s wife too. This may be taken as a source of Trimalchio’s vulgarity, but it seems to be the way in which Trimalchio frequents his delicati that is considered tasteless, showering him with gifts and showing him too much affection. But Trimalchio having a delicati in itself is not considered vulgar, in fact the main character of the Satyricon has a younger male lover himself!
The emperor Domitian was known for having a puer delicati, Earinus, who is openly praised in the contemporary literature. For example the poet Statius compared their relationship to Zeus and Ganymede, who in mythology was a young boy known for his looks, swept up by Zeus to Olympus to serve as his cupbearer. Statius also wrote other poems favourably describing these relationships for other contemporary elites. In Statius’ poetry there is a clear affectionate relationship between the master and his delicati, in direct contrast to Trimalchio who for similar affection seems to be portrayed as vulgar or distasteful.
So the conclusion about how Romans viewed these types of relationships is a bit contradictory! But we can make some conclusions that will be applicable to Nero:
With this in mind let’s turn to Nero. Unfortunately no contemporary accounts survive that discuss the incident and how the Roman’s reacted, and so we are left to look at how later accounts perceived the incident to make an assumption of how the moment lingered in the popular imagination at the time.
Our two main accounts are Suetonius and Cassius Dio. Suetonius emphasises the castration, and how Nero made Sporus wear a bridal veil for a wedding and treated him as a wife. We are not sure exactly how common it was to castrate delicati but the fact he emphasises this for Nero suggests it was part of what was surprising about the incident. But of course the most “scandalous” part is how Nero treats Sporus as a wife, both breaking the gender roles and subverting Roman expectations of the purpose of marriage - Nero here seems to be marrying out of lust (discussed a bit below). Later in his account Suetonius also says Nero was married to his freedman Doryphorus, and here played the woman’s role himself, “imitating the cries and lamentations of a maiden being deflowered” (point 29). Here Nero’s submissiveness, especially to a former slave, completely usurps the perceived “norm” for these sorts of relationships. As Caroline Vout explains, both the incidences with Sporus and Doryphorus were shocking in the sense that Nero has subverted the “natural order” of things, which is a recurring theme of his account of Nero.
But Cassius Dio offers a different focus, in his account Nero marries Sporus because he resembles his late wife, Poppaea Sabina, whom Nero had recently Murdered. Dio tells us that Nero would call Sporus “Sabina” and it was because of their resemblance that Sporus was castrated. Dio then tells us that Pythagoras (possibly they Doryphorus mentioned in Suetonius) also shacked up with Nero; with Pythagoras acting as Nero’s husband and Sporus as Nero’s wife. (Dio, 63.13.1) Interestingly Dio tells us that this marriage took place in Greece, and that the Greeks celebrated the event as they might a festival. They even made prayers that Sporus may bear Nero children (to which both Dio and Suetonius relate a joke that the Romans use to say about the incident, where they wished Nero’s father Domitius had married a wife like Sporus instead of Agrippina - I.e they wish he had never been born). We perhaps here see the different cultural perceptions of the incident, in Greece the event was not seen as shocking as in Rome.
After Nero’s death, Sporus then became an associate of emperors Galba, Otho and Vitellius during the civil war that followed - Vout suggests he went then from “bride” into imperial mascot, offering some form of legitimacy to their reigns by association with Nero.
As to the incident of “marriage” between Sporus and Nero - I don’t know much about homosexual marriage in Rome but contemporary poets Juvenal and Martial both offer criticisms of this form of marriage. This ties into two big ideas around the concept - namely that Roman heterosexual marriages traditionally served a purpose for childbearing or cementing family ties, and so a marriage that cannot bear children is perceived as one solely done out of lust (tying into Suetonius’ comments on Sporus) which goes against Roman virtues and morals. Secondly there is a connection with “Greekness” or more loosely barbarity - Juvenal and Martial connect these types of marriages to Greek philosophers - ridiculing them for claiming intellectual authority whilst at the same time giving into their desires. This may then tie into Dio’s connection of the Sporus incident with Greece - the Romans saw Nero’s marriage to Sporus within the context of him abandoning his Roman-ness in the pursuit of Greek artistic and cultural pursuits.
So we can assume the Romans would have reacted to Nero’s marriage to Sporus in certain ways relating to their own understanding of marriage and relationships between men and puer delicati:
Hope this helps in any way! Some books on the matter:
Caroline Vout, Power and Eroticism in Imperial Rome
Edward Champlin, Nero
A quick book search also turned up: Transantiquity, cross dressing and transgender dynamics in the Ancient World (which I haven’t read but may be of interest!) https://books.google.co.uk/books?id=sC0lDwAAQBAJ&printsec=frontcover&dq=Transgender+Rome&hl=en&sa=X&ved=0ahUKEwjh8PGM8fHoAhUrNOwKHbiHCSgQ6AEIOzAD#v=onepage&q=Transgender%20Rome&f=false