The best source for German churchbooks (for those of us in the U.S.) is the Family History Library in Salt Lake City, or its many branches throughout the country.I am not aware of many of them being available online, though I would hope that that may happen over time.
If you go to familysearch.org, you will see a tab labeled "library" at the top of the page.Clicking on this, you can access the library catalog.I put "Roedgen" in the search field, as that seems to have been the main community where J. Arnoldt Alt & relatives lived before emigrating.Unfortunately, all that popped up is a place in Luxembourg, whose French name evidently equates to Roedgen in German.I'm guessing that maybe there's also a Roedgen across the border in Germany, but evidently the Family H. Library doesn't have a copy of its churchbook.
As for Neukirchen, it appears that there are about a dozen communities with this name spread from Oldenburg (NW Germany) to Austria.I checked out the ones in the Rheinland, but hit no paydirt.The FHL has films of the churchbooks of several Catholic parishes with that name, but no early Lutheran (Evangelisch) ones.This suggests that the one you want has not been filmed.
I suppose that maybe this really is Neuenkirchen, of which there are two parishes of that name in Westphalia (Westfalen).Regrettably, here again the FHL only has the Catholic churchbooks, for both places.I don't have a good map of the German landkreis system (counties), so I'm not sure whether either of these two places-- one in landkreisSteinfurt and the other in Wiedenbrueck -- is the same as the one that appears NW of Zweibrueken in the map in Mrs. Burgert's book (see below).
If you go to the "search" tab at familysearch.org, you can call up the Ancestral File entry for Johann Arnoldt Alt and Anna Catharina Reinschmidt.I did this by plugging the marriage year of 1731 into the search field, and using just Anna Catharina's first and last names, along with her spouse's surname of Alt.
Clicking on the name in the Ancestral File entry for this couple, you'll see the detail on which Randy Davidson's post was evidently based.It also shows the name of the person who submitted this information.Possibly he may be able to help you with the source.I'm not certain that he's related to the Alts.I got the impression that he may have come at this from the Reinschmidt side, but at least he should have some clue as to how he got the information from the churchbook.
Often the best method is to hire someone to go to the Lutheran Church in the community or to the local archive and look the information up.The old German script can be difficult for those who have not studied the "Gothic" handwriting that was standard in Germany until recently.However, in some towns (like Schwaigern, home of my Hoffarth ancestors) the data from the early books have been transcribed and typed up so that it's very legible.
Notwithstanding that the Alts were apparently Evangelische in Germany, you should not necessarily rule out a search of Catholic records in Roedgen or nearby communities.People were required to adhere to the religion of their local ruler regardless of their own views.
I have an ancestor -- Casper Poppelsdorf -- who was from a German town ruled by a Catholic prince.When, upon arriving in England, he answered Queen Anne's call for settlers in America, he was asked his religion.He answered "Catholic."Even though this answer was probably without great conviction, it was the "wrong" answer, as Queen Anne and her ministers had no interest in building up the Catholic population within her realm.A few years later, Casper tried again to emigrate.This time, he gave the "right" answer (Lutheran), and was allowed to come to New York.
If you have access to any of the books by Annette Burgert, her introductions provide good background information to the subject of German immigration in the 18th century.Her "Eighteenth Century Immigrants from German-speaking Lands to North America, Vol II, the Western Palatinate," covers the general area where the Alts evidently lived.At page 275 of that book, she notes that "the confiscated property of Abraham Roland was released to his sister Maria Elisabeth, the wife of Simon Alt of Einoed," a village in the Saarland (i.e., near Luxemburg) just northwest of Zweibruecken.Also, she notes that in 1609, one Jacob Alt was located at Erdesbach (a short distance east northeast of Kusel).