No, you're absolutely correct, Darlene: it is complicated. That's why we have to do the research to figure out if something is, or might be, under copyright.
Works created in the U.S. that were in the public domain on 1 January 1978 (when the 1976 Copyright Act took effect) remain in the public domain and cannot subsequently be copyrighted. This has some fairly far-reaching impact upon genealogy reference websites and services and, given that 1978 date, even traditional genealogical libraries.
But backing up a bit--and remember, I am not a lawyer--in copyright terms "published" generally means the date a work is offered for distribution (or actually distributed) to the public, whether by sale or other transfer of ownership, or by rental, lease, or lending, with no explicit or implicit restrictions on the disclosure of its contents.
The granting of copyright protection requires that the original work be of a certain type. The U.S. Copyright Office states: "Copyright, a form of intellectual property law, protects original works of authorship including literary, dramatic, musical, and artistic works, such as poetry, novels, movies, songs, computer software, and architecture." Remember my example of compilation copyright? The USCO goes on to say: "These categories should be viewed broadly for the purpose of registering your work. For example, computer programs and certain 'compilations' can be registered as 'literary works'; maps and technical drawings can be registered as 'pictorial, graphic, and sculptural works.'
I don't want to know anything about the church records you're using (because then I can't be accused of providing legal advice if I don't know anything 
), but a few observations:
The records range from 1871 to 1903 and, by that and simply by the fact that they're church records, I assume there is no individual author of record. Meaning that if there is, in fact, an unpublished status that meant the records could still have been copyrightable under the 1976 act, then it is the church who would have an arguable case about copyright ownership.
Copyright is granted to the original author of a creative work, or to an entity which has contracted it as a work-for-hire. For instance, a ghost writer might sell an "autobiography" as a work-for-hire so that the celebrity is the author of record and therefore can register copyright. However, once copyright is established, even if I were to sell "All Rights" to a book, I am still nominally the copyright holder even though I have no rights left to exploit.
You can't register for copyright a "found work." In other words, if at a yard sale I stumble upon a never-before-seen manuscript written in 1890 by John Smith Jones about the Jones family and their migration to Oklahoma, I can't copyright it. It isn't my original work. I could go in and, quoting very liberally from the manuscript, write my own version of the events and copyright that. But copyright applies only to original work by a human (which is the rationale for the very recent publication by the Copyright Office detailing why no AI generated work is eligible for copyright).
The upshot of those three items is that--if copyright is in effect for the records, and it's a big if--it can only be the church who holds of the copyright. It could have transferred all rights to FamilySearch (highly unlikely), but FamilySearch was not the original creator of the work and would not hold the copyright. A compilation copyright regarding the way they present the information on their website or in their library, maybe; but not an original copyright of the work.
That these are church records--and I assume not records that the church considers private, such as financial information--my bet is that the church has made the records available to parishioners and the public for a very long time. But I can't know that. However, the first photocopier hit the market in 1959. If the church ever let the record books themselves be borrowed, or photographs taken, or photocopies made, then arguably they would have been published.
The Copyright Act of 1909 granted protection only to works published with a valid copyright notice. Accordingly, unpublished works were protected only by state copyright law, and even published works without proper notice fell into the public domain. The copyright term was 28 years with an optional renewal for another 28 years.
Unpublished works are, by definition, those which have not been distributed in any manner. Prior to 1978, copyright protection at the federal level was available only for published works. After 1978, copyright protection became available for both published and unpublished works. For works created before 1978 that were published or registered before that date, the initial term of copyright remained at 28 years from the date of registration or the date of publication with notice. At the end of the 28-year term, the copyright could be renewed optionally for another 67 years for a total term of up to 95 years.
Because so much of copyright revolves around a human creator, works created before 1 January 1978--but never published or registered by that date--are generally protected by copyright law for the life of the creator plus 70 years. For unpublished anonymous works and works where the death date of the creator is not known, the potential copyright term is 120 years from the date of creation. If it was Deacon John Smith who hand-wrote all the entries in those church records for a couple of years and he died in 1952 and those records could never have been considered to be published...public domain. The records you're looking at span 1871 to 1903. Coincidentally, 2023 is 120 years after 1903.
Again, far, far from legal advice. But without delving further into it, it's difficult for me to imagine a scenario where FamilySearch has any claim of copyright over images of the church records.
