No, there wasn't. Guiliani supported domestic partnerships (which conferred very limited benefits) when he was mayor of New York City. Afterwards, he supported civil unions but not marriage equality; and supported a federal constitutional ban on equality in the event 5 or more states got gay happy. In 2011, long after he left office (and stopped campaigning for President) Rudy took the position that the marriage equality should be left to the states, but also criticized the New York Legislature for legalizing same-sex marriage. In other words, he does not support gay marriage.
The rest of the article is even more idiotic and dishonest (falsely accusing an actor of calling Republicans Nazis), but once you recognize that the dolt is lying about his main example of a tolerant G.O.P., there's no reason to waste more time on the dolt.