Looking at their webpage, I’d have to guess that Fatima is right.
I’m sorry I need some help here:
From their website:
4. Catholic Charities agencies are authorized to exercise their ministry by the diocesan bishop. Whether founded by a diocese, parish, religious congregation, or lay activists, Catholic charitable works and institutions have their formal Catholic identity in relationship to the Church and the diocesan bishop.
The bishop is charged in Church teaching and canon law with responsibility for the apostolate within diocesan confines. However organized in terms of canon and civil law, Catholic Charities have responsibilities to operate consistently with the teachings and values of the Church. While there is great organizational variety, the local diocesan bishop ordinarily is positioned within the civil law structure—even of a separately incorporated Charities—to allow him to exercise his canonical responsibilities for the apostolate.
That doesn’t jive with a renunciation of their Catholic identity. I can’t speak to the homo/abortion thing.