Brotherdan,
I would agree that we should carefully monitor our own attitudes in this regard so we aren't simply branding as "false Christians" people with whom we disagree on some minor doctrinal issues. However, I believe that Paul is telling us to exercise sound discernment when he writes in 2 Corinthians 11:13 that there are "false apostles, deceitful workmen, masquerading as apostles of Christ."
It seems to me that if there can be false apostles there can also be false Christians.
I think the term "false Christian" would apply, for example, to person who professes to be a Christian who "comes to you and preaches a Jesus other than the Jesus we preached… a different spirit from the one you received, or a different gospel from the one you accepted (2 Corinthians 11:4)."
I'm not saying that a genuine Christian can't be misled. However, I would say, for example, that a person who claims to be a Christian but says that he has never been reborn spiritually (John 3:3) is contradicting himself. (Yes, I understand that the Watchtower teaches that a spiritual rebirth only applies to the 144,000. I believe that's one of the key doctrines that separates them from historic Christianity.)