There are a lot of things which people do that are against what I believe as a Christian. I find nowhere in the the teachings of Jesus that I should reject anyone other than those who don't want to be accepted. Some people, not just Christians, will not accept that same sex attraction is not a choice. Church leaders in institutional organisations which have rules around such things have two options: give up their position, or break the rules and accept people into their congregation in a loving and accepting way and face discipline. There will always be limits. Someone who is a habitual thief will be counseled against that behaviour and if they persist in that habit there will be some church discipline as well as anything that the legal system might bring.
Sexual preference is very different. Someone who is attracted to people of the same sex cannot just 'give up', but for me, I would ask them to read the Bible for themselves and come to a conclusion as to how they should live with integrity before God. I know people who are same-sex attracted (including church leaders) and each has come to a different conclusion as to how they should live: either living together or living a life of celibacy.
You have asked a very serious question and I'm glad people are explaining different approaches to how those who seek to follow Jesus find different ways of being faithful but true to the way that God has made them.