No, they don't. To use your (and Jesus's) analogy of the sick needing a doctor, those people rejected the treatment. There's no need to be in a hospital or a doctor's office if one rejects the treatment. Those people may as well go to some quack who will tell them what they want to hear because they are in denial about their condition.
And BTW, just because the remaining members did not make a show of walking out it does not mean they are not likewise sick and in need of a physician. The Bible is quite clear that all are sinners. The gay lobby and their fellow travelers simply refuse to see homosexuality as a sin.
I have seen churches where those who feel disturbed by the Holy Spirit leave and those left in the pews sit smugly and say “Good, they didn’t need to be here anyway.”
And the church withered and died because the purpose of the church is to go and find sinners and let the Holy Spirit work.
Yes, the seeds may be choked by weeds or fall on fallow ground, but we must still scatter the seeds where there is nothing planted.
I notice that the pastor in this article and the church members aren’t saying “Good, they need to leave”, rather they are saying “The word of God needs to be preached, and sinners need to repent.”
And that is the right attitude to have. A call for repentance, not joy that sinners are leaving the church.