To grasp why Parliament passed a law in 1701 forbidding a Catholic from acceding to the throne, you need to understand a little of the era's power politics. The Stuart dynasty had long flirted with Catholicism. But James II, who became King in 1685, was prepared to go the whole way. He had to go, and in 1688, James was deposed by an alliance of powerful aristocrats.
The 1701 Act of Settlement was intended to prevent him, or his Catholic heirs, ever coming back. It entrenched Britain, which would go on over the next two centuries to become the most powerful and influential nation in the world, as a Protestant power.
So how might things have been different had James II not been deposed and the Act of Settlement never passed? The "Glorious Revolution" of 1688, in which James II was deposed, cemented the authority of Parliament and put permanent curbs on royal power. Many regard it as the seed from which liberty and democracy grew, not just in Britain but around the world. Without it, Europe might have been weighed down by sclerotic Catholic tyranny.
Then there is economic development. The German sociologist Max Weber identified a "Protestant work ethic", in which capitalism sprang from this particular religious philosophy. Perhaps if Britain had been ruled by a Catholic dynasty there would have been no Industrial Revolution.
All that is an interesting thought experiment. But it cannot be taken too seriously. Resistance to royal tyranny was growing across Europe anyway (and exploded spectacularly in the 1789 French Revolution). And Weber's theory of capitalism has holes. It fails to account for the extraordinary business acumen of Europe's Jews. History would certainly have been different if Catholics had not been excluded from sitting on the British throne for these past 300 years, but perhaps not as different as we might imagine.