In my limited experience, it seems that the pro-same-sex marriage party would be helped if Christians would use the word “repent” more often when preaching the gospel. They hear us say “we are all sinners” but then they hear us challenge a particular sin. So they wonder, “why is this one sin being singled out? If you have sin, and I have sin, who are you to call out only my sin?” If we are not clear about repentance, then they do have a valid argument.
Be clear about the life, death and resurrection of our Lord. Be extremely clear. The gospel is the power of God for salvation. The Holy Spirit gives new birth through the preaching of the gospel. Be clear about the gospel.
Then call people to repent and believe. As long as it is clear that repentance and faith are responses to the gospel, no one can ever rightly accuse you of a works-based gospel. Repentance involves work, but it is work that is in response to the gospel of justification by faith in Christ alone. And it is work that only the Holy Spirit can bring about in true believers.
We are not worried that every sinner in the church is unsaved. Everyone in the church is a sinner. We are worried that unrepentant sinners are unsaved. Welcome all sinners to call you out on unrepentant sin, then call out others for the same. Then the only charge someone can bring is that you are being consistent.