That sums up the essence of Catholic teaching in one spiffy sentence.
Here’s the more fullsome quote from. Cardinal Burke :
We welcome them as children of God, as brothers and sisters of Christ, but we don’t welcome their lifestyle, so to speak, or the way in which they are living. And so if you have, for instance, two men or two women who are living together openly in a homosexual relationship, yes, you care for them, and perhaps “care for pastorally” is the better expression. You care for them but one has to be very careful in the Christian community that the impression is not given to the rest of the faithful that somehow their relationship is morally right and that the Church welcomes that relationship too. No, it doesn’t. (Source)
And homosexuals aren’t being singled out here either. The same would apply to lyers, drunks, gossipers, fornicators, thiefs, lazy people, dirty mouths, etc. It applies to everybody because every single person has sin in their life. Yet, while every person is welcome and given spiritual support, their sinful lifestyle must change.
Person ≠ lifestyle
It really isn’t all that complicated.