It is hard to be a supporter of gay rights and be a church worker in a conservative church. I was in that situation myself. I was a teacher in three different Lutheran Schools (LCMS) for 24 years.
I would like to say that when I "came out" as a gay person that all was well, but it did end up with me losing my job. No one had any complaint about my work or my character. They were sad to see me go, but go I must nonetheless.
You say, "There really doesn't seem to be a place where I can be a Christian and a supporter of people's rights." That is a really sad commentary on the state of Christianity isn't it? Why are Christians not the most supportive of people's rights?
You are a youth minister. You work with gay youth all of the time even if you don't know who. Many of those young people are struggling with being gay in a culture that condemns them for something they had no choice in nor control over. The trauma and suffering inflicted on gay youth by homophobic churches and families leads to a great number of suicides and a immeasurable emotional anguish. It is my opinion that those of us who are Christians have an obligation to let young gays know that they are loved and welcomed. We need to assist them in establishing healthy, loving relationships.
Sometimes doing the right thing is hard and has its cost. I have never regretted being honest with people about who I am. There was a cost, but the freedom I have felt is of much greater value. I wish that all of our young gays could have that freedom and acceptance.
I would recommend you watch two DVD's if you haven't already seen them. For the Bible Tells Me So and Fish Can't Fly.
I am now quite involved in the Episcopal church and am very much accepted and loved. I had hoped that one day I would hear from some of my former students who later in life would tell me that they were gay also. Just a few months ago that happened. I hope those students will feel comfortable about calling them Christian AND gay and not need to apologize for either.
Tu Amigo, Pablo
For I am convinced that neither life nor death...neither the present nor the future nor anything in all creation will be able to separate us from the love of God that is in Christ Jesus our Lord. Romans 8:38-39