There is an interesting piece in the most recent "daily dispatch" from Zenit on the practice of giving blessings to those who do not receive Holy Communion during the communion procession. Apparently--and I was unaware of this--it seems to be the practice in some places to invite everyone into the communion procession and then give a blessing of some sort to all those who do not actually communicate.
First of all, it seems to me that a distinction needs to be made. I am familiar with the practice of blessing children who have not yet reached the age of first Holy Communion. This makes sense to me. I do it myself and have even seen it at ultra-traditionalist Masses in the Extraordinary Form. Had these children been born into one of the Eastern rites or Orthodox churches, they probably would have received Holy Communion already.
Adults, however, who are members of separated ecclesial communities, or who do not believe in Christ or even God, or Catholics who have placed themselves outside of communion by their own choices, are all another story. Each Good Friday we are reminded of the intensity of our prayer for all these categories of people with whom we are not yet in full communion.
Christ's salvation is for all without exception. In this sense it is inclusive. That we are not in full communion with one another here on earth is a manifestation of the sins of history and the bad choices of persons. (And I can't help but think here of those who are publicly anti-life.) These failures of ours and our ancestors are not absolved by the cheap and easy values of being "inclusive" and "welcoming."
It can be very uncomfortable when only some can come to Holy Communion. Perhaps it's a wedding or a funeral in which--by the world's standards--only a few seem to actually participate fully in the ritual. It goes against the over-arching niceness of being "welcoming."
But there is a kind of welcoming and "inclusiveness" that relieves us of our discomfort and makes it look like public sin, heresy, or schism don't matter. We can do this blessing-for-all thing in the communion procession and everyone "gets" something, whether it be Holy Communion or a nice blessing. We are "inclusive," and "open" and "accepting," and we feel good about ourselves and warm and fuzzy about our ministry. The wounds of sin, so manifest in the imperfection of our communion with one another, are covered over and forgotten. We no longer have to worry about the hard work that full communion with one another would require, of the changes that might be demanded of us and the penances we might find we owe to each other. No way. Penance and change are from another era. We are "inclusive" and "accepting."
That we are not in perfect communion with one another ought to make us uncomfortable. But if we medicate ourselves against this discomfort by indulging our own need to be nice and "inclusive," we absolve ourselves of the difficult and often uncomfortable work of restoring true communion.