She only changed to keep votes so she could keep her position. She supported "traditional" marriage because it was the leading popular opinion. If you watch how she does things, she only supports what has the most support. She has no actual moral or philosophical reason to oppose or support gays, it's all how much she wants to stay in office.
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https://www.washingtonpost.com/blogs/the-fix/wp/2013/03/18/how-hillary-clinton-evolved-on-gay-marriage
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http://www.theatlantic.com/politics/archive/2014/06/hillary-clintons-gay-marriage-problem/372717/
. and in her own words
https://www.youtube.com/watch?v=6I1-r1YgK9I