OK, let's go through what you have and see if we can fill in any of the missing pieces.
Both born in Montreal (city of, I'm assuming) ca. 1850. Do you have any actual birth or baptismal records on them?
Family involved (possibly) in a Church squabble...maybe over their role in construction of a cathedral.
Settled in Saginaw (city of?), Saginaw Co, MI 1882.
So then come the obvious questions:
Where were they married and do you have a copy of the marriage license or parish record?
Which parish did they belong to in Michigan?
Have you pulled their obituaries and death certificates?
In order of birth, what were their kids names (there was an actual naming convention back then that can really help sort things out).
Were any of their kids born in Saginaw? If so, do you have copies of their baptismal records (helps identify brothers and sisters/other relatives of the parents).
In any of the parish records in Michigan, does it mention any other parishes where either of them received any of their sacraments? (This is usually scribbled in the margin and you'll usually find it when they were married in the Church, but at a parish other than the one where they were baptised or confirmed.)
Of the kids born in Michigan, is there any mention of other parishes where they received sacraments?
Next question is whether there's anything to the building of the cathedral story.
According to the Canadian Conference of Catholic Bishops, there are 12 dioceses in Quebec, plus Montreal and Quebec City. Since there's usually only one or two cathedrals per diocese, that means if there was a problem, it would be at one of these:
1) Amos . . . doesn't fit the timeline.
2) Baie-Comeau . . . doesn't fit the timeline.
3) Chicoutimi . . . doesn't fit the timeline.
4) Gaspé . . . doesn't fit the timeline.
5) Gatineau-Hull . . . only now celebrating its 40th anniversary...can't be part of the pic
6) Mont-Laurier . . . doesn't fit the timeline.
7) Moosonee . . . doesn't fit the timeline.
8) Québec . . . see below
9) Rimouski . . . doesn't fit the timeline.
10) Rouyn-Noranda . . . doesn't fit the timeline.
11) Saint-Anne-de-la-Pocatière . . . the cathedral was built in 1751
12) Trois-Rivières (and Nicolette)...The Cathedral in Trois-Rivières is about the right age (actual date of its construction isn't noted on their website) and many French-Canadians who settled in the Saginaw valley were from the TR area.The diocese of Nicolette wasn't founded until 1885...so they can't be a factor.
13) Joliette (where the Essexville Taceys originated) . . . St. Charles Borromeo Cathedral
As for the city of Montreal proper:
The Basilica-Cathedral of Notre Dame was built before either of your ancestors were even born.
The Basilica-Cathedral of Marie-Reine-du-Monde of Montréal was definitely controversial enough...but the time frame doesn't fit. The real controversy over its construction was really between the archbishop,Mgr Jean-Jacques Lartigue, and the Sulpicians. Now there is a lot of history between the Sulpicians and the Tessier family, but none of it friendly in the 19th century. The big suit had just been settled by the Crown and the Tessier's lost. It would be hard to see how your family could have taken sides in any of it ca. 1870 and had any negative fallout because it was settled more than 20 years earlier. The rest of the controversy over the building of the Cathedral had to do with the architect telling the archbishop that his scheme to recreate the Vatican in Montreal was unreasonable. Work on the cathedral didn't begin until 1875.
The Co-Cathedral of Saint-Antoine-de-Padoue de Longueuil wasn't built until the 1880s and it really didn't have any controversy about it that I can find.
It was built at the right time, though its location is not a traditional area for members of the Tessier family...at least not that I've come across. So if it is this family and this is the right cathedral, there wouldn't be a big difficulty finding records on them since there wouldn't be a deluge of Tessiers to sort through.
Also, since Quebec City is such a well-documented area, any records of the cathedral are well-preserved and the archdiocesan archivist should be able to help you get information on the rebuilding in 1865 and any major disputes that arose.If there was a formal excommunication, then the archivist can also help you locate those records.
OK, hope this is enough to start. If we can fill in the blanks and cross reference with the Loiselle Marriage index, we should be able to get you back to the 17th century.
PS, I recently moved to Midland. If you're still in the Saginaw area, I'd be happy to meet up at the LDS center and see what we can accomplish. Let me know.