What PoD would be needed so that British parliament weren’t so prejudiced against James VII & II’s Catholicism?

French and Spanish peasants were better off than their Irish counterparts.

Also, realistically speaking, an England in which James II stayed in power would neither be "absolutist" nor "dominated by the Catholic Church". Parliament and Protestantism were both too well-entrenched for such an outcome.

I fully agree, in fact according to some historians, James' idea would have been very similar to the one used by the Wettins a few years later, that is, when they converted to Catholicism to become king of Poland, while simultaneously remaining rulers of a strongly Lutheran nation, in practice he wanted to create a commission that had to discuss and guardianship over the Anglican church, while he would work with them to create a third branch between the high and low churches, with the aim of reintegrating dissidents and assimilating refugees from the continent ( mainly Lutherans fleeing the wars of Louis XIV ) in practice it was an agreement where he partly delegated his power as head of the church in exchange for concrete support for his government ( so much for the sovereign with absolutist delusions, Eh ! )