the Stuarts weren't all Catholic, just James II. This wasn't popular (though not actually illegal at the time, I don't think); so various lords and parliamentarians invited William of Orange to be king (he was married to James's daughter), and James fled. His son and grandson - the old and young pretenders - did try to raise armies and recapture the throne, but failed.
Starbuckone, the English had already got rid of the royal family - James's father - but this was also felt to be unpopular and has not been tried again