How did Islam encounter and interact with other religions?

Answer 1

It all depends, as in any religion if it has the power it will by its nature obliterate by force if need be any other region. A good example of this is the vandalism committed in the name of Allah in Afghanistan. Or the ban on Christian literature as you enter Arabia.

Answer 2

In its very earliest years, when Christianity was small and vulnerable, it appears that Christians treated other religions with respect. There were arguments over who was right, with pagans and Christians making claims and counterclaims of miraculous events. But at this stage, if the pagans claimed a miracle for one of their gods, this miracle was not disputed, but a more stupendous miracle was brought forward to demonstrate the power of Christianity.

Some of the early Church Fathers exchanged correspondence with the Roman emperors. Although this correspondence was largely concerned with privileges or freedoms sought for the Christian faith, it must be remembered that the emperor was also the head of the Roman faith.

As Christianity grew both more confident and more assertive, this changed.
The pagans were to become incensed at the rashness of Christians who presumed to accuse their countrymen of error, and who insisted that their ancestors were suffering eternal misery simply because they had been pagans.

Of course, Christians had been at loggerheads with the Jews since apostolic times. Edward Gibbon (The Decline and Fall of the Roman Empire) says that under the reign of the Christian emperor Constantine and his successors, it was not long before the Jews experienced the bitterness of tyranny. The civil immunities which had been granted or confirmed by Severus were gradually repealed by the Christian princes; and a rash tumult, excited by the Jews of Palestine, seemed to justify the lucrative modes of oppression which were invented by the bishops and eunuchs of the court of Constantius.

The emperor became the real head of the Christian Church, and Constantine instituted the beginnings of the long persecution of the pagan temples. After Theodosius made Christianity the official religion of empire at the end of century, all notions of religious toleration were abandoned. The pagans were persecuted with a fury unimaginable in previous centuries. To help justify the Christian persecution of the pagans, the Church Fathers built upon their traditions of persecution under the pagans. the ecclesiastical historians, Eusebius indirectly confesses that he has related whatever might redound to the glory, and that he suppressed all that could tend to the disgrace, of religion.