There is a strong (but not absolute) correlation between a preference for the Latin Mass and retrograde, harsh beliefs that are not in keeping with Catholic teaching.
The “other thing” you mention, I’m guessing, is the Society of St. Pius X, an organization founded after the Second Vatican Council that rejected the reforms of Vatican II and believed the vernacular Mass to be invalid, and also thought that Pope John XIII and subsequent popes were (maybe) not valid popes, because of their supposed deviation from eternal truths. The SSPX actually started consecrating bishops and ordaining priests in defiance of Rome, and were ultimately kicked out of the Church (sort of), and thus became schismatic. There’s an ongoing effort at reconciliation with the SSPX, but they’re a nasty bunch. They absolutely believe that all non-Catholics are not saved, and they have truly unsavory beliefs about the Jewish people. One (at least) of their bishops has openly denied the Holocaust. It absolutely would not surprise me if they believed that there was some sort of stain upon the soul of children born out of wedlock.
There are other (not schismatic) groups within the Church that also may believe that salvation is only for Catholics, or that children born out of wedlock are damned, or that divorced women should be banned from taking communion (even if they haven’t remarried). Opus Dei comes to mind.