Dividing the world into "Pagan countries" and "Christian countries" is both inaccurate (Jews weren't considered pagans) and overly-simplistic (state religions aren't a solid, fixed thing, especially over large areas before modern communication). While the Arab conquests were significant, not every Muslim country was converted "by the sword": there's even debate over whether the Muslim citizens of the early caliphates were, since such a small group, while large enough to conquer, would surely find it tricky to police the day-to-day behaviour and practices of so many people. (The Mongol Empire didn't manage to eliminate the practice of Islam in the areas under its control, despite ritual washing being punishable by summary execution, so it's plausible that Islam is just that persuasive.)