I was recently told about a Lubavitch family who only eats Lubavitch shechita.
What is unique about Lubavitch shechita? Are there particular opinions which they are stringent for that no one else is? Or is it just ethnocentric?
The Shulchan Aruch says that one may only eat from a shochet that has yiras shamayim (fear of heaven). Since this is a matter of a person's character that you cannot simply test, one solution is to only eat from shochetim that one knows personally and trusts. In old-world shtetls where everyone in the village knew everyone else, this was a common practice. In towns where chassidim lived, they often insisted that the town shochet be a chossid to ensure that he would be G-d fearing. In today's world of industrial mass-production, the consumer often has no idea what kind of person has performed the shechita on their meat. Therefore some Lubavitchers, although certainly not all, rely on some admittedly superficial indicators to help ensure that the shochet has yiras shamayim. Studying chassidus and going to mikvah every morning demonstrate that they are putting in an effort to advance in their worship of G-d, and refusing to cave to the pressure from American society to shave one's beard demonstrates that they are not easily swayed from their convictions.
I heard that there was some advancement in knife technology and the Rebbe (or a predecessor) saw that it reduced the consequences of failing to check and re sharpen the knife so he decreed that he would only eat meat slaughtered with this type of knife. This is what initiated the concept of a separate chabad shechita. According to the questions below, there are also theological differences about the shochet's intent.
There are two related questions here Why do people get Chassidishe Shchita?