Many Dems have lied about their support of rights, whether they be for gays or another group.
Biden, for example, has said that he ALWAYS supported gay rights when he clearly hasn't. Biden routinely lies about everything. We aren't talking about being hyperbolic, but pure lies.
Obama has lied and taken credit for things done in Illinois while he was not in state government.
Ted Cruz is an example of a Repub who has changed his mind on gay rights. He admits he changed his mind and didn't always support gays. That is the polar opposite of how Dems deal with their previous hatred of gays.