My friends kneel at Mass for the consecration of the Eucharist even when that particular parish is not accustomed to doing so. The same applies with bowing before receiving the Eucharist. It is my understanding that all parishioners should assume the same posture as a sign of unity. Who is correct?
You are correct that a common posture during the Mass is a sign of unity, but it is your friends who are observing the correct posture (kneeling) during the consecration.
The General Instruction of the Roman Missal states:
A common posture, to be observed by all participants, is a sign of the unity of the members of the Christian community gathered for the sacred liturgy: It both expresses and fosters the intention and spiritual attitude of the participants. (GIRM 42)
To that end, the GIRM instructs that the faithful:
should kneel beginning after the singing or recitation of the Sanctus until after the Amen of the Eucharistic Prayer, except when prevented on occasion by reasons of health, lack of space, the large number of people present, or some other good reason. (GIRM 43)
Also, not for the sake of unity but out of reverence, the GIRM instructs, “When receiving Holy Communion, the communicant bows his or her head before the sacrament as a gesture of reverence” (GIRM 160).