One definitely cannot be LDS and Catholic or Mormon and Catholic. Perhaps some people are in the process of converting, I don’t know. I never noticed that myself.
As for the rest, one has to remember that early Christianity spread across cultures and began to develop organically in each place. In some areas Christianity died out and in others it flourished. This happened over and over again over time, with essentially five major spiritual and liturgical traditions becoming dominant.
The Latin tradition (Roman Catholicism) happens to be the largest of these in north America today but is just one of several.
It may help to see a map of the Roman empire from approximately the time of Christ.
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Christianity spread across the empire along the good roads from city to city, but also crossed over the borders into further regions, like India and Persia. In fact the first kingdom to actually formally convert was not Roma, but Armenia! The practices and prayers of Armenian Christians differs somewhat from what you may be familiar with.
https://jspivey.wikispaces.com/file/view/Map__spread_of_Christianity_to__12th_century___medium.jpg
Eventually Christianity spread to Abyssinia, India and even China by the seventh century.
Ancient Egyptian temple once converted into a church
Christian stele, seventh century China
At one time, uniformity was highly prized, and there was this concept that all Christians should pray and worship using the same forms. The trouble is that everyone thought their own way was best! So that did not work out too well, there were a lot of hard feelings over that.
Today we are a bit more enlightened, and we now place more value on the diversity of Christian expression than in the past.
http://www.armenianchurch.net/news/photos/Aleksy.jpg
Patriarchs of Armenia and Russia
Others may post a long list of all the churches that are in communion with each other, but that is not really necessary. Just remember that there are many types of liturgies and these originated in diverse places, but all see their origins in the work of the Apostles, while professing what is essentially a common Faith.