One is baptized into the visible Church, yes, so we count them as members ("non-communing" members until they are catechized and have made a credible confession of faith - then the Lord's Table is open to them). They are our covenant children and therefore Christians in the same sense that Jewish children are called Jews according to Romans 9:4-9. Also one may be outwardly Jewish, yet Paul writes,

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He is not a Jew who is one outwardly, nor is circumcision that which is outward in the flesh. But he is a Jew who is one inwardly and circumcision is that which is of the heart, by the Spirit, not by the letter; and his praise is not from men, but from God (Romans 2:28-29 NASB).

As Jewish children partake of all the covenant blessings their parents enjoy and are called Jews, so our covenant children enjoy the covenant blessings that we enjoy outwardly: The Apostles' teaching, breaking bread, prayer, the oversight of Elders, etc. When they give credible evidence of inward regeneration, conversion, and discipleship, they are accepted as communing members.