The Bible clearly says that Jesus ate with tax collectors and sinners, and sinners meant sexually active prostitutes or whatever and homosexual people who aren't repentant of their actions. And so, clearly, we should not cut ourselves off from relationships with anybody who is an unbeliever if we can by any means share the love of Christ with them.
But this is describing a person who, without any sense that his Christianity is being imperiled, or his soul, is acting out homosexual desire in sexually active ways. And, in order to avoid censure, he has gone to a church that endorses it.
I think we should abstain from fellowship with that church and abstain from fellowship with him, because the Bible says that if your brother does a certain sin then have nothing to do with him. Withhold your fellowship with him.
In other words, you have lunch with him—one final decisive lunch—and you say, "I've really enjoyed having you as a friend. This really grieves me. I'm willing to fight with you to the bitter end to help you war against your sin, just like I would like you to help me war against my sin. But if you make peace with your sin, you're doing what Romans 6 says you can't do as a Christian. And therefore you're acting as a non-Christian, and you're claiming to be a Christian. And the Bible says that I'm not supposed to have anything to do with you, not even to eat with you. And so our friendship is going to have to be broken if you go on like this."