The longer I do genealogy, the quicker I am to doubt any of the family folklore that gets passed down. The Taceys in particular are full of incredible stories...and only one of them has turned out to be true.
Personally, I'd be dubious that anyone changed their names in order to get back into the Church. That would come out of a real misunderstanding of excommunication. A single person will be excommunicated until they recant their heresy. A whole family doesn't get excommunicated. And all someone has to do if they are excommunicated is to recant and make amends with the bishop. It also doesn't make any sense that just changing their name would fix anything, because before any of them could get married or buried in their new parish, the priest would have to write the parish where they were baptized to confirm they were Catholics in good standing.
I also doubt the fight with the Sulpicians played any role in 1870. Back around 1840 the fight was settled with the British Crown ruling in favor of the Sulpicians. The whole thing was dead until the late 1920s when a couple of attorneys resurrected it and created the Corporation Tessier-Lavigne. They knew the suit was a scam because it would fall under the standard of "double jeopardy", since they didn't have any new evidence at all.
It's more likely that Casey fit well in the community. It was easier for Americans to pronounce and to spell correctly. The shift from Tessier to Tacey was made by the census takers because they simply couldn't handle the French accents so they wrote things phonetically. In Bay County, the census takers turned their lists over to the county and the property records of the homesteaders came off of the Census roles. So whatever was registered there got recorded with the Register of Deeds. Hence, their name was changed and they didn't fight it. Old Prosper was escaping a few problems of his own and I'm sure it was much easier to pick up his life on this side of the lake with a different spelling.