The Eucharist is meant to be a source of unity, not an experience of division. This is what we affirm at every Mass when the presider says to everyone present: "The communion of the Holy Spirit be with you all."
The Eucharist proclaims that the real bond of union between Christians is the mystical experience of being enlightened, inspired, moved, and guided by the indwelling presence of the Holy Spirit in each one's heart.
The "Communion of the Spirit" - trying to be united on the level of faith instead of divided on the level of its expression - is the starting point and the goal of the process: love that seeks unity. Our shared divine life is the theological basis this love is built on, the doctrine of faith that helps us understand the deep relationship we have with all who know Christ.
This communion is not perfect. It was not perfect in the early Church, and it is not perfect now. But to be aware of who you are through your divine relationship with God - Father, Son, and Spirit - is a mystical experience. A fresh look at the Mass summons us to look for and to deepen this communion wherever and with whomever it might exist.
Take action: Engage in conversation with a friend, co-worker, or acquaintance who does not share your faith tradition. Really listen to that person's experience of faith and see if you can find common experiences. When you have some quiet time, reflect on the conversation and see if you feel some bond of unity based on the common experience of faith.