[Zeneta]

The libertarian argument is in favor of gay equality.

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

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Completely false.

[ansel12]

What is false about it, libertarianism discriminates against non-heterosexuals?

[RginTN]

The libertarian argument is in favor of gay equality. 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
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Completely false.
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Not completely false. From the Libertarian party platform pro-gay marriage:

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. http://www.lp.org/platform