These suggestions crop up all the time - that a Catholic England would be some sort of united utopia.
It ignores whether the Catholic church survives naturally (Henry VIII not breaking with Rome - granted an annulment by Rome or Catherine of Aragon gives birth to a surviving male heir for example) or whether it is restored (Henry VIII changes direction and restores relations with Rome, or Edward VI is given a Catholic education, or Mary has issue or Elizabeth is raised Catholic and has issue) by encouragement or by violence.
Both those changes ignore what is happening elsewhere in Europe - how influenced England would be by a Protestant Netherlands (a major trading partner), or a Protestant Scotland for example (a Catholic England is not necessarily going to help the Stuarts against a bottom up reformation anymore than the Protestant Elizabeth was willing to support Protestant rebels against a Catholic Monarch in OTL).
A future Catholic monarch could marry a devout Lutheran or Calvinist (if real politics dictate such a union) just as Charles I married a devout Catholic in OTL - that would unsettle and disturb people - a woman who might influence her children against the established religion of the realm.
Nor does it take into account whether a future Catholic monarch is going to offer some kind of edict of tolerance to allow Protestant citizens freedom of worship which might lead to a groundswell of change or result in its revocation forcing mass emmigration damaging the economy etc.
The Civil War which led to the establishment in the Glorious Revolution and a limited Parliamentary Monarchy - was not purely based on religious grounds - it was equally about an increasing dissatisfaction with a monarchy that was trying to rule on a very narrow band of support.
Whilst the monarch's position within the church of England caused additional problems removing that one aspect does not necessarily prevent a future monarch in a Catholic England facing revolution or rebellion.
Like the Church of England the Catholic church supported monarchy in many cases Absolute Monarchy across Europe and was not at the forefront of defending the common people against an authoritarian and remote government.
The divisions within England are not just based on areas where the Catholic church survived longer and it is hard to argue that a population would have been more united under a Catholic establishment any more than an Anglican one.
After all both churches would on the whole be made up of establishment figures, people from similar backgrounds and who would support the status quo rather than support political and social reform - Some Anglican bishops were quite prepared to argue against outlawing slavery, women's votes, civil marriage and the married women's property act in the 19th Century (I doubt Catholic bishops would have been any different).
The north did not remain completely Catholic for centuries, its separation has more to do with its distance from London in a country that was becoming increasingly centralised, areas distant from the centre of power are often great breeding grounds for dissent and that is why the North like Wales and the South West became fertile recruiting grounds for Protestant dissenters such as the Methodists and Quakers, just like grinding poverty in newly industrialised cities across England caused dissatisfaction and a disconnect from political elites.
The so called political divide doesn't really stand up - large swathes of rural England continue to vote Conservative in both the North and South, just as large parts of London vote Labour as their city-living compatriots in the north do. In most post-war elections many voters have directly switched from Labour to Tory and vice versa.
Catholic oppression in England was as much the result of outside actions by Catholics as it was the result of a Protestant government determined to eradicate it.
In almost every country in Europe where the Catholic church survived as the dominant religion it did its utmost to maintain the status quo, to crush opposition and to prevent or delay social and political change and reform.