I am a Knanaya Catholic, I can help you with this. Basically in the history of the Nasrani or Syrian Christians of Kerala there has always existed a rift. Two groups of Christians existed, the Northist who lived in the north of Kodungaloor and the Southist who lived in the south of Kodungaloor. The Northist are the descendants of those who were converted by St. Thomas and the Southist (Knanaya) are said to the be descendants of Thomas of Cana a missionary merchant who settled in Kerala with 72 Judeo-Christian families in the year 345-800?. For this reason both groups attest to be of different ethnic groups and also had much animosity for each other in the past and also lived endogamously of each other.
Now Knanaya history is hazy, the Thomas of Cana story may or may not be true. It is based on a very old legend and a very strong folk tradition of the Southist (Knanaya). This folk history was first written down in the 1700’s by a Syriac Orthodox bishop by the name of Mar Gavril, this document is still available to view. Also, Thomas of Cana is said to have received a copper plate with the privileges him and his people received from the then ruling king. There are written records from numerous sources stating that indeed a figure by the name of Thomas of Cana came to Kerala and won over many converts for Syrian Christianity, however these sources are vague on whether or not families came with him.
For cultural differences, the Knanaya hold to ancient folk songs and wedding traditions that we have zealously maintained for centuries. It is interesting to note that these folk songs and traditions are extremely similar to that of the Cochin Jews of Kerala. A Cochin Jew scholar by the name of (late) Dr. P.M Jussay, wrote two extensive texts on the similarities of the two cultures.
I have posted many Knanaya folk songs on my Youtube channel: (Below are my favorites)
The St. Thomas Christians (Northists) follow the ancient way or “margam” of St. Thomas the Apostle. They have numerous cultural traditions distinct to them and were considered a very high caste people in historical Kerala. The priest and Syriac scholar Fr. Joseph Palckal made a great English documentary on the St. Thomas Christians. This is the video below:
As for shared traditions both the Knanaya and St. Thomas Christians dance the Margam Kali and celebrate Pesaha or Passover on Holy Thursday. We also share the liturgies of West Syriac and East Syriac.
As for the question of marriage, the Knanaya still maintain the tradition of endogamy. If a Knanaya marries a Syro Malabar or anyone else Non-Knanaya, he or she joins the diocese of said spouse. The Knanaya are not against the Syro Malabar Church, there are just a few very vocal people in my community who are die-hard endogamist and feel that the Syro Malabar Church is taking away this right of marriage.