What makes us Catholic? Does dissent from the Church’s social teachings, for example, put one outside the Catholic faith?

Strictly speaking, a Catholic is a person who has been baptized in the Catholic Church or has been received into the Church after a valid non-Catholic baptism.

The Catechism of the Catholic Church states:

Fully incorporated into the society of the Church are those who, possessing the Spirit of Christ, accept all the means of salvation given to the Church together with her entire organization, and who—by the bonds constituted by the profession of faith, the sacraments, ecclesiastical government, and communion—are joined in the visible structure of the Church of Christ, who rules her through the Supreme Pontiff and the bishops. Even though incorporated into the Church, one who does not however persevere in charity is not saved. He remains indeed in the bosom of the Church, but “in body” not “in heart.” (CCC 837)