There is a first difficulty in the use of the word "inclusive" here. The word can have two distinct senses, and, typically for the debate about LGBT issues, the word is used in the letter to the Times in a way that does not distinguish between the two senses. The outcome of this failure to distinguish is an unjustified presumption that "inclusion", poorly defined, should become a characteristic of the life and practice of the Church.
If the object of the term "inclusive" is persons, then one can quite rightly say that the Church should have an openness to everyone, as persons, regardless of their origins or lifestyles. Pope Francis' use of the term "accompaniment" expresses something of this idea.
If the object of the term "inclusive" is the teaching of the Church on matters of marriage and sexuality, then it is quite another matter. And the meaning is quite different. It is the assimilation of this second sense to the first sense in the common sensibility of both Christians and others that is the unfortunate, and, I suspect, intended consequence of failure to distinguish between the two senses on the part of pro-gay advocates.
A first reflection, from the point of view of Christian life, arises from the moment of Baptism, the Sacrament by which a person becomes a member of the Church. The Baptismal profession of faith expresses a turning away from sin and a turning towards the person of Christ, a conversion of life. That call to a conversion of life asks those who enter the Church to live a changed life, not just at the temporal moment of Baptism but existentially in the subsequent living of the Christian life. Each individual might face that call in a different specific manner, and so the specificity of that call experienced by a person who identifies as LGBT will differ from the specificity of the call for a person who has, say, pursued a life of crime.
A second reflection arises from considering whether or not the Church should use the term "inclusive" to describe its nature. According to the Compendium of the Catechism of the Catholic Church, n.166:
The Church is catholic, that is universal, insofar as Christ is present in her: "Where there is Christ Jesus, there is the Catholic Church " (Saint Ignatius of Antioch). The Church proclaims the fullness and the totality of the faith; she bears and administers the fullness of the means of salvation; she is sent out by Christ on a mission to the whole of the human race.This is more fully developed in the corresponding paragraphs of the Catechism of the Catholic Church, nn. 830-831:
Secondly, the Church is catholic because she has been sent out by Christ on a mission to the whole of the human race:
All men are called to belong to the new People of God. This People, therefore, while remaining one and only one, is to be spread throughout the whole world and to all ages in order that the design of God's will may be fulfilled: he made human nature one in the beginning and has decreed that all his children who were scattered should be finally gathered together as one.... the character of universality which adorns the People of God is a gift from the Lord himself whereby the Catholic Church ceaselessly and efficaciously seeks for the return of all humanity and all its goods, under Christ the Head in the unity of his Spirit.It is clear, I think, that the Church describes herself as "catholic" or "universal", and does not use the term "inclusive" to describe her own nature. I would suggest that, in responding to the misguided claim in favour of an "inclusive" Church, we should instead respond with an account of the catholic, or universal, nature of the Church.