The Right Revd Mark Davies made the comments in a pastoral letter issued to his diocese last weekend.
They come after Pope Francis recently called an Extraordinary Synod on marriage and the family, which backtracked on wording in a report which was seen as an unprecedented welcome to gay people.
A draft version of the report said gay people had "gifts and qualities to offer" the church, and that same-sex relationships can provide "precious support."
However, these phrases were omitted from the final version of the report.
It also changed the titling of a paragraph from "welcoming homosexual persons" to "pastoral attention to people of homosexual orientation."
Right Revd Davies said in his letter:
"God's plan of marriage, which is written into human nature and raised by Christ to be a Sacrament, is being replaced by the idea that we can each make our own truth according to our own ideas and desires...
"The first Christians required great courage to overcome and transform a vast, pagan world whose ideas about marriage and sexual morality were not unlike those which prevail in our own culture.
"Today we need this same, supernatural, courage to give witness to all the Church believes and teaches about marriage, the family and human sexuality.
"The Church offers the truth she has received from Christ her Lord, not with hostility towards those who have taken a wrong path, but with the greatest love and concern for every person.
"The Church on earth is made up of sinners called to become saints; our practice of frequent Confession is, indeed, a constant reminder that every one of us is called along this path!
"It would be the ultimate failure in pastoral care or charity, to mislead people by encouraging them to remain in sin, or fail to call them to repentance and renewal...
"Today I want to dispel any misleading impression that the Church will abandon her witness to the truth and change her teaching in the face of hostile trends in public opinion or the destructive ideologies of our time."