Everyone wants to belong. The desire to be longed for is part of being human. And, underneath it all, it's a desire to be longed for by God.
God's plan is that this desire should be met in part by others. As Pope Benedict wrote in Deus Caritas Est:
Seeing with the eyes of Christ, I can give to others much more than their outward necessities; I can give them the look of love which they crave.
I get the impression, though, that most American Catholics simply assume everyone else knows they belong, and so make no special effort to ensure those around them feel like they belong. (Meanwhile, a small but vocal minority go about deciding who does and who doesn't belong.)
At any given Sunday Mass, there might be a handful of people who don't really feel like they belong, but who feel like they should feel like they belong. Most of the people around them, though, don't give them a look of love so much as a polite nod. And any organized attempt to reach out to those who don't feel like they belong will fall most heavily on those who do feel they belong, and who will resent the implication that they might not. "Why is someone welcoming me to my own church?"
The solution, I suppose, is to see with the eyes of Christ.