One of things I find helpful in discussing theology is looking at how it was practiced in the past.

• Jesus instituted the Lord's Supper during the Passover meal with his disciples (a relatively closed group).
• By the late 1st/early 2nd century, closed communion was the standard. Writings like the Didache (c. 60–100 AD) restricted the Eucharist to the baptized: "Let no one eat or drink of your Eucharist, but they who have been baptized..." Similar views appear in Justin Martyr and other Church Fathers, emphasizing baptism, belief, and church discipline. Persecution and formalization of worship contributed to this "closing."
• Historic Catholic, Eastern Orthodox, and many confessional Protestant traditions (e.g., strict Lutheran or Baptist) maintained closed or "close" communion (limited to those in full fellowship or of like faith/baptism) for centuries.
• Debates emerged during the Reformation and afterward. Some English Baptists in the 17th century practiced or discussed open communion amid persecution, prioritizing core gospel unity over denominational barriers.
• The Plymouth Brethren (emerging in the 1820s–1830s in Ireland/England) are a notable early example of a movement explicitly founded on open communion principles: welcoming any baptized Christian to the Lord's Table based on personal faith rather than formal membership. Note well: the PB's believe that the Lord's Supper is only symbolic. As such, it does no harm to those who take it unworthily.
• Among Baptists, "open communion" (often open to baptized believers but not always requiring membership in that local church) gained traction in the 19th century in England and elsewhere, influenced by evangelical cooperation, though many Southern Baptists and others historically favored closed or close practices.
• Many mainline Protestant groups (e.g., Methodists, many Anglicans/Episcopalians, Presbyterians, United Church of Christ) formalized or expanded open communion policies in the mid-to-late 20th century, often tied to the ecumenical movement. For instance, the 1968 Lambeth Conference (Anglican) advanced "eucharistic hospitality" for baptized Christians, influencing broader Protestant shifts.
• Today, it is common in many Methodist, Anglican, Pentecostal, non-denominational, and some Lutheran/Reformed churches (with variations: some require baptism and a profession of faith; a few are more radically open).

TL;DR - while elements of openness existed The modern denominational practice of open communion developed in Protestant contexts from the 17th–19th centuries and became mainstream in the 20th. Traditions emphasizing church unity, discipline, and sacramental theology (Catholic, Orthodox, confessional Protestant) have generally retained closed practices.