Why was Roman policy towards Christians so... haphazard and confusing?

The relationship between Rome and Christianity was rather complex. Here's a rough overview (I'm focusing more on the early Empire to the second century):

Roman religion focused heavily on ritual practice. It was essential to perform the right rituals in the right way at the right time and place. Even stumbling while performing a ritual portended ill. The performance of ritual ensured the pax deorum ("Peace of the gods") - a kind of contract, if you like, between the gods and Rome, whereby the Romans would honour the gods appropriately and the gods would support the Roman State. Thus, failing to perform the rituals threatened the pax deorum and threatened the security of the State. It was a political issue, as much as a religious one.

Religiously speaking, Rome demanded one thing only: that its subjects practice Roman religious rituals (e.g. attending sacrifices, honouring the Roman gods and the genius of the emperor). Rome didn't mind if its subjects worshipped other gods as well, as long as they fulfilled their civic duty by performing Roman religious rituals.

Judaism and, later, Christianity, however, were monotheistic and could not allow the honouring of any other god. While Christians saw themselves as being persecuted for their beliefs, the Roman State saw itself as protecting the State against, essentially, treason. Rome didn't exactly have anything against Christianity as such, it was opposed to the treasonous refusal to perform one's civic duty.

So, why might directives from the Emperor vary? Firstly, it's important to remember that many emperors didn't issue specific directives about Christianity (at least as far as we know). The issue was very frequently dealt with locally, by provincial governors (as Pliny dealt with it, although he did seek direction from Trajan). That means that there was always some variety in approach. In his reply to Pliny, Trajan even specifies "It is not possible to establish a general law which will provide a fixed standard".

Secondly, emperors dealt with the issue as it arose, to a large extent. Philo, for example, records an embassy to Caligula which reminded Caligula of Augustus' relationship with Jews:

He did not banish them from Rome or deprive them of their Roman citizenship just because they were careful to maintain their identities as Jews. He did not force them to abandon their places for prayer meetings, or forbid them to gather to receive instruction in the laws, or oppose their first-fruit collections ... if the [monthly grain doles] happened to occur on the holy sabbath ... he ordered the officials in charge of the distribution to set aside until the next day the portion of the welfare which belonged to the Jews.

A surviving papyrus tells us that the Jews of Alexandria sent their own delegation to Claudius over a dispute with the city of Alexandrians. This was considered inappropriate (for a sub-group to send their own delegation), and Claudius organised a compromise (along the same lines as Augustus) between Alexandria and its Jewish population, threatening the Jews with persecution should the Jews ignore propriety in that way again. This was dealing just with Alexandria, because that was the issue at hand (although it indicates something about Claudius' attitude more generally, and he strongly implies general persecution should the Alexandrian Jews ignore his decrees).

Also, consider the specific needs of each emperor. Nero, for example, was to a large extent looking for a scapegoat to blame for the Great Fire of Rome in 64 CE. This may help explain why the persecution was only in Rome (there was ill feeling towards Nero as a result of the Great Fire, and deflecting blame onto Christians served to defuse that).