The episode of Doctor Who “The Romans” from the William Hartnell era only intersects tangentially with religion, but it does so in interesting ways. The Doctor and his companions end up in Rome in the time of Nero, and the Doctor actually gets mistaken for a lyre player who has been invited to Nero’s palace. He inadvertently gives Nero the idea to set fire to Rome, leading Vicky to upbraid him for always telling them not to meddle with history, when he clearly is contributing to it.
The fire in Rome was almost certainly not set by Nero, who is reported to have aided in the efforts to put the fire out. (He certainly didn’t fiddle while Rome burned). But the rumor that he was responsible circulated nevertheless, and Nero then used the Christians as a scapegoat. And so the idea that the Doctor was responsible for the first official imperial persecution and execution of Christians is somewhat disturbing, even considered within this fictional story world.
Then again, later Christian authors would surely have emphasized divine providence in this – the blood of the martyrs being the seed of the church. And so the Doctor might also be credited with the spread of Christianity as well.
The one explicitly Christian character is Tavius, a man who is kind and upright, and who is towards the end of the final part of the story shown fingering a cross that he wears as a pendant. The cross as jewelry is of course an anachronism. Nevertheless, after having seemed to ignore Christianity altogether, the revelation that one particularly positive character was a Christian is powerful and provocative.