As optimistic as it may be for the 'freedom of religion' stuff in the Constitution, remember that in the 1770s-80s Americans were vehemently anti-papal...even more so than the British in some respects.
Patriot/Framer leadership was highly interested in getting Quebec as part of their Great Experiment, it is to be expected that they exercise their rather considerable leeway to rein in anti-papal feelings. Much of that feelings (eg. about the backlash the Quebec Act got) was outrage about the Quebecois getting a perceived preferential right for colonization of the Ohio-Mississippi Valley.
American Quebecois could never have the foreseeable numbers or influence to dominate the other states through the federal government, the only way anti-papal radicals could rally a considerable popular following against them among the Protestant majority, that would scare the Quebecois away from the Constitution.
Respect for civil rights and state autonomy was deeply ingrained among WASP settlers, only a tiny bigot minority is going to argue against the right of Quebecois to make sensible use of their civil and state rights in a state where they are the overwhelming majority, or worse, in favor of denying equality to Catholic Americans. The only big problem would arise if the Quebecois try to abuse state rights to discriminate against Anglos and Protestants.
If they kept Quebec, they're probably not going to be able to convince the Canadians they've done a good enough heel-face turn that their culture is safe.
The original US Constitution, especially with explict guarantees I mentioned, gives an exceeding ample autonomy to national minorities that are majority in one or more states. I'm puzzled to see how the federal government's powers, in the original restrained pre-ACW interpretation, could be used to "oppress" their culture. This is centuries before mass media, so in the lack of purposeful assimilationist policies from the central goverment, the danger of spontaneous cultural assimilation is rather remote.
As I said, there are most likely going to be guarantees about church establishment and language, so it can't be Quebecois being forced to use English before federal courts or in interstate commerce. The Catholic Church is getting her establishment, and French newspapers are sacrosanct, as is French education.
Beyond that, the local elite probably won't like the stronger centralization under the Constitution.
So the Quebecois shall get Federalists and Anti-Federalists. That makes them no different from other agrarian WASP states.