If you believe the Bible is the word of God then you cannot be a gay rights supporter. The problem here is that many mainstream churche$$$$ not only condone same sex marriage but also allow their clergy to be gay.
You have accurately diagnosed the problem. This is why we are swimming upstream when even churches are telling gullible parishoners that homosexuality is a good thing, we're expecting political solutions from a spiritual problem.
First, clean up the churches.
These are the "churches" that are the most likely to promote homosexuality and virtuous. This is the list of the National Council of Churches which is an extremely liberal group.
African Methodist Episcopal Church
The African Methodist Episcopal Zion Church
Alliance of Baptists
American Baptist Churches in the USA
Diocese of the Armenian Church of America
Christian Church (Disciples of Christ)
Christian Methodist Episcopal Church
Church of the Brethren
The Coptic Orthodox Church in North America
The Episcopal Church
Evangelical Lutheran Church in America
Friends United Meeting
Greek Orthodox Archdiocese of America
Hungarian Reformed Church in America
International Council of Community Churches
Korean Presbyterian Church in America
Malankara Orthodox Syrian Church
Mar Thoma Church
Moravian Church in America Northern Province and Southern Province
National Baptist Convention of America
National Baptist Convention, U.S.A., Inc.
National Missionary Baptist Convention of America
Orthodox Church in America
Patriarchal Parishes of the Russian Orthodox Church in the USA
Philadelphia Yearly Meeting of the Religious Society of Friends
Polish National Catholic Church of America
Presbyterian Church (U.S.A.)
Progressive National Baptist Convention, Inc.
Reformed Church in America
Serbian Orthodox Church in the U.S.A. and Canada
The Swedenborgian Church
Syrian Orthodox Church of Antioch
Ukrainian Orthodox Church of America
United Church of Christ
The United Methodist Church