There appears to be a high degree of religious tolerance, which is not typical of Earth's past.
I think you missed the part where newly converted Stannis had heretics-including family members-burned at the stake.
That said, there isn't wide-spread religious tension of the sort we saw in the middle ages thanks mostly to the circumstances in this particular period of history. The Andal invasion and their imposition of their religion of the Seven on Westeros was millennia ago and until recently the faith militant had been disarmed for centuries.
At the time the books take place, religion in Westeros has taken a back seat to politics as the Septum was rendered impotent by the Targaryens. There's no great schism within the faith or large scale opposition from an equally influential outside religion, mostly because the Doom of Valyria shattered Essos into (until recently) mostly independent city states around the coast beset by emboldened marauders that dominate the continent's interior.
The "tolerance" of the Old Gods in the north seems mostly just old pagan traditions dying hard and nobody in the south caring enough about what stubborn think, so long as the Septum tithes keep rolling in. In short, it's less an overall philosophy of religious tolerance and more a case of the apparatus of organised religion being to weak to do anything about it.
I suspect this was by design on the part of GRRM, presumably because he didn't want to deal with that aspect of medieval history.
The High Sparrow wasn't depicted as hating other religions as far as I recall; he primarily wanted to drain the swamp of King's Landing.
His immediate goal certainly, though I'm sure he would have gotten around to seeing to the body once the head was free of rot.
He may have been outwardly humble and softly spoken but don't forget the violence and oppression he ordered against those he deemed opposed his goals. Don't think he wouldn't have dealt with Red priestesses and priests and their congregations any less harshly, given the opportunity. That movement had holy crusades and pogroms in the making written all over it.
There are quite a few theories from the book material that the Maesters may have conspired to get rid of the dragons and other forms of magic in previous centuries in order to bring about a "reign of reason."
I tend to view the Order of Maesters as being a parasitic organisation, with no larger agenda beyond self perpetuation. Certainly at some point in the past they were driven by some basic goal to spread and preserve knowledge, but the inevitable mindless bureaucracy has long since taken over any such purpose, leaving it pretty stagnant.