You either do not understand the Catholic religion, or you do not understand the gospel. I am going to assume that it is the former, as this is usually the case.
The Catholics do not teach salvation by faith apart from works. They salvation by merits, some which come from self, some which come from the saints, Mary, and their false version of Jesus.
You needn’t assume either (it’s usually the safe be, anyway). I think that you are correct that Catholics do not teach salvation by faith alone. They teach much about salvation through the Catholic church. My point was that the gospel is still there, beyond the false teachings, the dogma, even the “Catholic church.” This is a difference between other cults mentioned. Would I call the Catholic church “Christian”…no, I wouldn’t. There is too much departure from Christianity.
Some would argue that the CoC does teach a works based salvation because the act of baptism is the point where you are saved. I believe that they do in their teachings regarding maintaining that salvation…but that’s another issue.