While the Divine Liturgy is indeed the major form our unity takes as Orthodox Christians, it is not the basis.
More about that formless basis in a moment, but for now I'd also like to insert the observation that our unity has many other forms than only the Divine Liturgy. It shows up also in shared customs and disciplines such as fasting together at set times, the prayers we have in common that we pray when we are apart. We also have a vast shared literature, especially the Holy Bible and the Creeds and the
conciliar decrees and Fathers.
But the unity of the Church is none of these, singly or combined. They are its forms and they do indeed serve to strengthen and promote our unity, but they are not what produces it.
The secret of unity in doctrine is unity in Life, with an upper-case L.
It is what St. Paul calls "a great mystery", the mystery of Christ and the Church, into which mystery every catechumen is initiated by Holy Baptism, the mystery whose fulfillment and consummation is the goal of an Orthodox Christian's life.
The secret of unity is that we each share with the Risen Lord that same, intimate, personal relationship the Apostles shared with the same Risen Lord. (Yes, that sharing takes place, supremely but not exclusively, in the Divine Liturgy.) That is a spiritual reality not to be reduced to any visible thing or set of visible things.
It means the meaning of my life, now, is Christ. I look at my brother and sister and see that the same Christ Who is my Life is also his and her Life. It is as if we all had our straws dipped into the same drink, the Fountain of Immortality, or were all branches of the same Vine, planted in the same soil, the same Life (sap, nutrients, etc.) circulating through us all.
We look at each other and see another *self*--another hypostasis of one and the same nature we hold in common, that re-created human nature which exists in Christ alone, that He created by uniting, in His Incarnation, what had been human nature with His Divine Nature, by putting to death on the Cross the mortal aspects of the new human nature in Him, by glorifying it in the Resurrection and deifying it in His Ascension into heaven.
That new human nature, which is united to the Divine Nature and is Christ's alone -- but into which you and I, in a great mystery, can be incorporated. It's the living of the Life that is His, the Divine-Human Life, the eternal Life, that doctrine describes and serves. False doctrine describes our Life in Christ/Christ's Life in us badly or not at all; true doctrine describes and serves it well.
He who lives that Life knows the difference. That's the secret to doctrinal unity.