No, liberals haven’t been lying to libertarians, Libertarians hold their political positions because they believe in them.
This is ordinary, run of the mill, everyday, libertarianism, it is among the things that separates them from traditional America and conservatism, and God.
“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.”
Ahem, well, it turns out that the Holy See didn't like American (19th-century) liberalism, didn't like its Congregationalist and Calvinist roots (in "the priesthood of the believer", a Protestant doctrine) and liberal (now conservative) devotion to the Liberty Interest of the American People, and most of all, the revolutionary existential threat it raised to the Spanish Empire, which as you'll recall was almost a co-branded operation of His Most Catholic Majesty and Holy Mother Church. But by the time of the Congress of Vienna, South and Central America were crawling with young Spaniards and criollos (New World ethnic Iberians) who'd read the French philosophes and imbibed hellish ideas from the intellectuals of the salon movement.
And so the Holy See sat down secretly with the representatives of Austria-Hungary (Prince Metternich) and Imperial Russia to explore ways to counter rising American influence and interest in freethinking among the endangered souls of New Spain, and the result was the secret codicils of the Congress of Vienna.
And so Great Britain and the United States promptly sat down and negotiated the Clayton-Bulwer Treaty, which promulgated what we nowadays call the Monroe Doctrine, which was an anti-Spanish, anti-European (at least as far as the Continental Powers), and anti-papist, liberal (conservative) document. We proclaimed the freedom of the New World from Old World influence and occupation, so there! Never mind that the British Empire and the Royal Navy were the principal guarantors of the spirit of the document.