Negative. That is the big L party’s platform. The little l position is generally “This is none of the government’s business and therefore should not be the subject of regulation.”
So libertarians disagree with this political position?
1.3 Personal Relationships
Sexual orientation, preference, gender, or gender identity should have no impact on the government's treatment of individuals, such as in current marriage, child custody, adoption, immigration or military service laws. Government does not have the authority to define, license or restrict personal relationships. Consenting adults should be free to choose their own sexual practices and personal relationships.