1. Baptism is the public face of Christian mission.
1.1. Most properly, the baptized are properly the public face of Christian mission. Their actions and identities are what the world sees. "You are our letters." 2 Cor 3:2.
1.2. Public reasoning progresses not from Christ but from the way that baptism liberates creation to be creation. It does not advance specific Christian reasons, a kind of knowledge that is only available to the baptized but advances a kind of solidarity.
2. Hospitality can only equally apply to the Eucharist if it does the same thing as baptism.
2.1. Sacraments are not uniform. They do not deliver the same "grace" or the same sort of thing and so they are related to one another and not just different delivery systems of the same goods. The medium is the message. Baptism does one thing, the Eucharist another.
2.2.1. Baptism welcomes.
2.2.2. The Eucharist reinvigorates, sustains, and holds forth the end of the baptismal journey.
2.2. Hospitality concerns invitation to baptism. Eucharist only follows after the welcome of baptism.
3. The Eucharistic liturgy has remain largely unchanged despite drastic changes in the public and private, in Christendom and now, after Christendom.
4. It would seem that the most hospitable act would be to welcome to the Eucharist without restriction but that would be to perpetuate the liturgy as warped by Christendom.
5. Thus, contemporary efforts to hospitality should be driven by a welcome of baptism.