Nitpick: "spread it with sword and fire" was literally from day 1 onwards - take a look at some history books that don't only gloss over the early days of Islam.
You are right that they did relax somewhat later on, once power in the newly conquered territories had been stabilised the hard way. Note that I said "somewhat", though: the inferior treatment of unbelievers did not only take the form of extra taxes: they were fundamentally second class citizens. Their testimony was not worth as much as that of a Muslim in court (if it was allowed at all), they were only allowed to own certain amounts of property (if that), could not intermarry with Muslims, and were more harshly punished for any transgressions - in particular, if the transgression had been inflicted on a Muslim.
This treatment was actually to a large part responsible for the "brain deflation" suffered by the Islamic empires the centuries after their establishment. After the very violent initial phase, religious minorities were treated sort of bearably - but not in a way that was really tenable in the long run. In the long run, lots of smart unbelievers converted, if only to save themselves the sort of hassle that their parents had to endure. And if there is one Achilles heel to actual Islamic culture (at least the old school version of it), it is that it is very poor at science and learning: once the old scientist caste of the Hellenistic culture they had taken over had converted, their technological and scientific edge evaporated over the space of only two generations or so.
Most of the fabled science of early Islamic empires was done by the people who had been doing science before the Muslim conquests: Hellenistic men of learning, i.e. unbelievers who were taken over from the old system. Quite a number of them converted, and had a quite reasonable working environment for their day and age. However, the supply of new scientists dried up after that: universities that actually teach people to think critically are not really wanted in a warrior religion that demands total obedience of its followers.
If you think that I am exaggerating, take a look at the atrocious performance of pretty much all higher education institutions in the Arab (!) Muslim world. I am emphasising "Arab Muslim" here, as the newfound Muslim conservativism you mention is most prevalent there. There are some Islamic states, like for instance Malaysia, that have functioning educational systems, and universities. But the cultural make-up of Malaysian society is fairly different from classical Muslim Arab culture.