It doesn't say Irish v Irish the differences were between catholics and protestants. It compares the rioting to the type common in Belfast. You don't seem to know about the history of that part of Liverpool I have both Catholic and Protestant ancestry and connections to the area so I've got local knowledge of what it was like. It's much better these days. For information about catholic chapels in Liverpool being attacked in the 18th century see the history of St Mary's RC Liverpool its early chapels were attacked by mobs:-
https://archive.org/details/catholichistoryo00burkuoft/page/n6
Blue
I do know something about the history of Lancashire and I also have Lancashire Catholics, CofE and nonconformists in my tree.
What do you mean by 'Protestant'? Do you mean your Irish ancestors or your English CofE ancestors?
Various places in 18th C. Preston and neighbouring villages (A mob from Preston). London, Liverpool. Probably other places.
Times: 1715 & 1745 Jacobite Risings; Jacobite Army occupied Preston 1716.
The Jacobite attempt at an invasion of England was led by an English landowning
Protestant MP, Thomas Forster. This rather weak attempt was met with little resistance in the north of England apart from the siege at Preston and even there the townsfolk were not heavily involved.
It wasn't a simple case of Protestant versus Catholic, far from it
1780 Gordon Riots which were a reaction to the Catholic Relief Acts. Gordon Riot was a recent topic on Melvyn Bragg's Radio 4 series "In Our Time", available on BBC iPlayer or BBC Sounds. The senior Catholic bishop in England had to go into hiding in London.
The Gordon rioters were multi denomination and even multi ethnic Londoners. The hanged leaders of the riot, which included at least 2 black people and a Romany Gypsy, came from a wide range of backgrounds and even included London Catholics. The primary objective of the rioters seems to have been looting, and was not driven by any religious or political concerns the participants had
The actual riot was opportunistic and had little to do with the original meeting/protest led by the Scottish Protestant nobility in the form of Lord George Gordon. Again another example of imported whipped up sectarianism. This time from heavily Protestant Scotland
The papal decree on marriage "Ne Temere" 1908 which required a Catholic to marry in presence of a Catholic priest caused ill-feeling.
I come from an English mixed Catholic and High Church background but have never heard of this before, so can't really comment
I've wondered if the reason why the marriage of my Scottish Catholic 3xGGF to my English C. of E. 3xGGM at St. Ignatius R.C. church, Preston didn't happen until the end of the month of her 21st birthday, 2 years after birth of their 1st child, was parental objection due to folk memory of 2 Jacobite armies marching to Preston. Their 2 sons were baptised C. of E. The 2 daughters might have been R.C. Great-granddaughters of Scottish 3xGGF were the trio who had 2 baptisms.
Or maybe 'folk memory' wasn't even considered, who knows? It's all speculation