I turned to two friends for help in answering your excellent question. One is the director of an outreach to those wanting to leave homosexuality, a man who is a former gay activist himself. The other is a pastor who was convicted of his judgmental attitude toward homosexuals, and sought the Lord's heart by involving himself in Exodus International and a local ex-gay ministry. Both of them wrote such great answers that I'm just going to paste them in here.
Unfortunately for us, because it makes it more difficult, mercy and judgment go hand in hand. The challenge is to know where to apply them both in situations that require both. With judgment, the Bible clearly calls us to judge sinful behavior. Especially if we are judging the behavior of other Christians. It isn't an option according to Matthew 18, and the Lord has blessed us with a model of how to approach one who is in sin. What we cannot judge are the motivations of the heart or a person's worth to God. It is hard for modern Americans to see that calling something sinful is an act of mercy. God was very merciful to us to show us not only the good things of Himself, but also the things He will not accept--which is also good. Others use the same words to condemn, but if we are mindful of our own sin and the mercy extended to us, when we are called to speak the truth in a situation, it will be delivered with such compassion and mercy that it will be an effective witness. Judgment comes in the words; mercy comes in the delivery of the message.
Here's an example of how to communicate:
"According to my spiritual convictions, homosexuality is sinful. I don't know what it is like to be gay or to have the feelings you do but I do know the loving character of my God. If He says, which I believe He does, that a certain sexual activity is sinful, then I believe that He says so because He wants you to have the very best in life and will make a way to meet the deep cries of your heart. I know for myself and my struggles with different issues, that what seems impossible to me is very possible for a holy and loving God."
As far as institutionalized Christianity, I don't know that any institution will change until the hearts of individuals change. Of course we must vote our conscience and speak what the Lord tells us to, but I think the main focus should be the person next to us. When we can look them in the face with love and compassion, nothing but positive change can occur. They may not like it at first, so we must be prepared to receive at least rejection and at most hostility--neither of which should move us past love.
With regard to activist groups, I don't suggest dealing with them as a group is a good idea. To be an activist means you are sold out to whatever you are fighting for, and as a group I think it would take another group to deal with them. If one is dealing with an activist, don't see them as an activist but as a saint of God in the making. Turn the other cheek, love them enough to hurt at the thought of their pain. I have learned that saying a small amount of appropriate truth and being a steadfast witness is the best way to witness to activists.
I am assuming from the tone that the writer believes homosexual conduct to be sin. S/he also seems to fear that if we aren't strong enough in our denunciation that gays will take over the public arena. If we show too much love and mercy it will be construed as acceptance. I understand that.
I just read a response J.P. Moreland made to Charles Templeton who was asserting that it is intellectually impossible to believe in God. Moreland pointed out that how the argument is framed is extremely important. If we accept a faulty premise we've already lost. This is what gay activists, with the collusion of much of the media, have done--for example, all those who do not accept homosexuality as normative are "homophobic." Of course this is linguistically and logically wrong. If you and I were homophobic we would never be around homosexuals willingly. But we also frame the argument incorrectly if we accept that.
So I would begin by saying that God showed me I wasn't responsible for how the world viewed what I do and say as long as it squares with His Word. Of course going by that Word can be dangerous; it can get you crucified. People, even religious people, may misinterpret what you do and say. As a fundamentalist I was always bothered by Jesus telling His disciples that the world would know they belonged to Him by the way they loved each other. I've come to see that I can love people without condoning or approving their actions--or their positions. But if my loving them consists of telling them "I am speaking the truth in love" or something similar it will not ring true. We absolutely must learn to see gays--and all other people--as people whom Jesus loves dearly. He cries out for them to come to Him. He wants them to know that no matter how far they drift, He longs passionately for them to come to Him. So, I began by realizing how much Jesus loved homosexuals-- including activists--and then because He was so pained by their sin and the cruelty of others, I found myself wanting to serve Him by helping to show them His love. I had to be Jesus in the flesh. I couldn't do that if my "love" was a veneer or simply putting on an act so I might get them to listen to my arguments. I had to decide if I really believed what God says about people who are separated from Him. Are they really basically empty spiritually? Can they really find true Joy apart from Him? If I really accept that then I don't have to argue with them that they really are or aren't happy, etc. I can simply proceed with the assurance that it is the task of the Holy Spirit to do that. My job is to love and speak the truth--gently for the most part.
______ (an outspoken gay activist) has been good for me in that regard. He has even asked me to appear with him at a Pflag (Parents, Families and Friends of Lesbians and Gays, a pro-gay support and activist group) meeting next year. He wants his side to see that someone can totally disagree with him (and them) and not be harsh or obnoxious. He and I have kind of a running joke that "I love ______ but we disagree totally on homosexuality." I do love him. He is well aware that I oppose gay marriage or adoption and acceptance of what we believe to be sin by the culture at large. I grieve over his views on homosexuality. But I am encouraged that thru lots of conversations and e-mails with some of the ex-gay folks, he has for the most part let go of his anger and bitterness toward the church and indirectly toward God. He now once again identifies himself as a Christian. I still pray that one day he will see the whole truth. But I know he wouldn't even be in a position to consider it if he had not seen God's love in the flesh.
I have heard the same kind of testimony over and over since getting involved with Exodus. Many of the leaders in Exodus ministries came to Christ because some Christian loved them. Most had experienced a lot of anger and rejection from the church and were bitter and antagonistic. It is imperative that we not allow ourselves to put homosexuality into a separate category from other sins. If we slip into that it will show in the way we relate and those to whom we are trying to minister will know it. For instance, do we oppose adultery and adulterers in public life with the same standard we use for homosexuality? I think we think we do, but I haven't seen consistency there. The bottom line is that we are in the business of reconciling ALL sinners to our Father. We must see ALL people as God sees them.