Here's at least a start on how Christians who hold these beliefs justify them.
Sodom was not about homosexuality. It was about rape and cruelty. All the men were involved in raping the two male visiting angels but not all of the men were homosexual.
And Ezekiel 16:49 explains the sins of Sodom as pride, over abundance, idleness, and not serving the poor.
Christians are not bound by Levitical laws and much depends on the translation process. Words can take on a different meaning in the translation process than what was intended. And for instance in 1Cor 6:9 and 1Tim 1:10 there are translations not using the word homosexual. The NRSV and RSV for instance use words such as fornicators, male prostitutes, sexual perverts, and sodomites.
Where Romans 1:21-31 speaks of natural/unnatural, what is natural or unnatural for the person depends on the person. For instance what would be unnatural for a homosexual, would be to engage in marriage with a heterosexual.
Consideration can also be given to the Bible as a product of its time and culture too. I don't think even many Catholics today on this forum would require for instance going back to the days when women were to keep quiet in churches.There are so many other things found in the Bible not practiced today.
It's a matter of faith and belief, of different theology and interpretaion. And given these types of undertanding, it could follow then if homosexuality is not a sin, pro gay marriage becomes a possibilty as well as does certainly the adoption of and providing loving homes for children by SS couples
No one here has to agree. But just hope this helps at least somewhat to give you a start in understanding and respectng the beliefs of others. Peace.