How does a Christian church justify (Biblically) performing a marriage ceremony for homosexuals? What is their interpretation of Scripture?

The biblical justification offered by those who perform such marriages often falls under the category of “common grace”. What is that? Simply put: That is the belief that there are some things God gives to all people, believer or unbeliever. (e.g. Matthew 5:45 says “the rain falls on the just and the unjust.”)

So to justify it as “common grace“, they would say something like, “Even people who have no regard for God at all have the 'right' to get married (heterosexual, homosexual, doesn‘t matter), because that is a ‘common grace’ available to every human being.”

Whether you agree or disagree with the fundamental issue isn‘t the aim of this answer because it wasn‘t the aim of the question. This is a "Biblical justification" given from those who care to justify it biblically.

The other answer given is: “The Bible doesn’t say homosexuality is sinful.” I know this is a sensitive and very culturally relevant topic today, and this particular issue has been debated and discussed incessantly. So I would encourage you to read Romans 1:18-32 for yourself. What does the Bible straightforwardly say about it?