Japan and Phillipines Legalizes Same-Sex Marriage in 2013

The challenge is then to make it more like Mexico, Brazil, or Argentina.

Maybe not have the Americans take over? But that would be a pre-1900 POD. The Church became bound up with an alternate identity partly in response to the American occupation, and this surged with their respobse to Martial Law after their initial support. In essence, you need to keep the Church seen the way it was in circa 1900. In essence, a longer anticlerical tradition.
 
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