The reason why only Roman Catholics are banned is that in 1701 it wasn't seen as plausible that a Christian would marry a Jew or a Muslim or someone from another religion.
Interesting that the wording is not "Roman Catholic" but Papist - which is a political statement in itself. Popes and their courtiers at that time were very political people which actively supported the disposed Stuarts, especially the Old Pretender against his sister and her husband who had taken the throne. The deposed Prince of Wales, only son of king James II/VII. and italian princess Mary of Modena, even died in Rome, his second son became a catholic cardinal.
So the rift within the Stuart family came from religious as well as political reasons - no wonder as it was a result of the Civil which sent James II. to exile in France where he became a believer in the Catholic church and changed his faith subsequently. His daughter on the other hand were raised as protestants on orders of his brother Charles II. (who only converted to Catholicism on his deathbed, having reigned as a protestant). So when James finally fathered a son with his Catholic wife, the political powers in England feared a "catholic dynasty" and invited William of Orange, son of Mary Stuart, princess Royal as eldest daughter of king Charles I. and husband of Mary Stuart, eldest daughter of king James II.
to invade Great Britain and take the throne together with his wife.
Problem was that neither of James II.'s daughters managed to have children surviving infancy, so the British politicians who had already fought hard against the Catholic opposition in the country, had to search for a non-catholic heir. As these were further down the line than Catholic ones (even after the male-line of James II. became extinct), they needed a law to legalize their protestant choice.
And to make sure that the Catholic influence did not come back through the king's bedroom, they forbid marrriages of future monarchs with catholic wifes.
So back in 1701 this law made sense.