"He loudly announced his status, that he has no intention of ever stopping his activities and that he does not consider them sinful."
What about the millions of heterosexual couples who are cohabiting (not married)? Most, if not all, don't consider that behaviour to be sinful. Should they all be kicked out of the Church? The pews will be awfully empty!
meant to say "cohabitating" not "cohabiting"
If they loudly make an issue of it ("Yes, we are fornicating; it's not a sin, but our right. Now shut up and give me communion!"), then yes, they should be denied full church membership, at least in a church that actually believes in something.
If, on the other hand, they admit that like everyone else they are broken sinners and want to be better, the church leader should be able to guide them into full membership.
The real issue, like always, is one of pride. Both the active homosexual in this story and your hypothetical fornicators demand that Christ take them on their terms. That's not what taking up the cross means.
As far as whether kicking out persistent fornicators would empty churches, I think you are over-estimating the numbers of the shacked-up in the pews. It's my experience that most of these folks (almost always young) have better things to do than go to church on Sunday mornings. I know I did. I had to first reach a decision to turn to Christ before I even wanted to go to church. I certainly did not demand a right to keep my sins. Why would I want to stay in slavery to sin when I was desperately trying to free myself (and I still am).
Maybe churches could do a better job evangelizing co-habitators (and sinners in general), but pretending sin does not exist is not the way to win souls for Christ. We should strive to actually stand for the Way, the Truth, and the Life. Christ came to set us free, if we will let Him. The Good Samaritan did not look at the beaten man, say "you're really not hurt" and then go on his way. We sinners are like that beaten man. Christ can heal us, but first we have to admit that we are broken.