I’m a tad late to the discussion, but…
There are as many different types of Mormon missionaries as there are Mormons. After all, just about everyone who is a Mormon spends time as a missionary. It’s not super likely that a Mormon will convert to something else while in the process of doing the 2 year missionary stint (I forget the actual name for it) but everyone has conversations, everyone learns things, and sometimes- depending on the person the approach what they hear and how they eventually respond- some people do wind up leaving Mormonism straight out or drifting away a little at a time within 2 or 3 years of finishing up their time as a missionary. Granted, a lot of them also return in great spirits, get married, and raise lots of Mormon babies, but there’s some of both and overall the retention rate for Mormons is not amazing. Not awful, really, but also not amazing.
Some Mormon missionaries are a brick wall, they do this intentionally and they know they’re doing it. But not everyone is like that, it’s case by case like it is with anyone else. It’s well worth asking if you really have an opportunity to get anywhere, and without knowing anything else but “This is a Mormon missionary,” the answer is “Maybe yes, maybe no.”
With that being said. For them as Mormons and you as a Catholic, the single most important point of interest is the Great Apostasy. There are some passages from Scripture that all of you may agree to look at, but the place you may want to focus on is early Church history. I recommend bringing up the names of the first three main leaders of the early Christian church (right after the apostles, but still well within the apostolic era…which you might have to explain a little bit). Clement of Alexandria, Ignatius of Antioch, and Polycarp of Smyrna. Introduce the names and perhaps a bit about what made them important. Here is the key point, though- focus in on how they died.
All three of these men were martyred. Some of the details are less than perfectly verified from a historical standpoint, but we do know for sure that all of the were martyred. Do some work on this history and be ready with it. This gives you a perfect opportunity to ask if these three men truly died for the actual Christian faith, or if they had fallen into apostasy and are therefore held in a different regard than any of their immediate predecessors who were also martyred. If you like, you can do a bit more research and come up with a few other people who were martyred for their faith at various points in time after these men too.
Even the nicest and most open sort of Mormon missionary is going to be a bit evasive, not because of any outstanding character flaws, but because the Mormon church is not super specific about when the Great Apostasy happened. It was pretty quick, apparently, but no one’s given any estimates in any official capacity. It’s kind of fuzzy, and this is a way for you to make history a bit less fuzzy and gently show why this matters and why it makes a difference. There is a way in which this can be shoved in someone’s face, but there’s also a way to tell some parts of the stories that belong to the ECF’s in a way that will actually be heard.
