"I'm one of those old-fashioned homosexuals, not one of the newfangled ones who are born joining parades"

Nathan Lane's quote is a humorous way of revealing his identity as a gay man. He is suggesting that he is not a "newfangled" gay person, but rather an "old-fashioned" one. This could mean that he is not a part of the more contemporary, visible LGBTQ+ community, or that he does not relate to the more flamboyant stereotypes related to being gay. It could likewise be a referral to the truth that he is a bit older, and has been out for a longer time period than a few of the more youthful members of the community. Whatever the case, it is clear that Nathan Lane takes pride in his identity and is comfy enough to joke about it.