The success had nothing to do with the Democratic Party. The Democratic Party didn't actively fight for those causes, mass movements did. Starting in the '70s the gay community started working to 'normalize' gay culture which led to more people realizing that many of their friends, families, and neighbors were gay. That removed the threat of the 'other'. Gay activists did that, not the Democratic Party. The Democratic Party pushed 'don't ask, don't tell' and, if they were feeling frisky, 'civil unions'.
Incremental progress which led to full marriage equality and military integration far earlier than anyone expected. The Democratic Party should be ashamed for killing gay rights like this.