Nonsense. The 14th Amendment doesn't create a constitutional right to commit sodomy, nor was it intended to do so.
Criminal sodomy statutes in effect in 1868: Alabama: Ala. Rev. Code 3604 (1867). Arizona (Terr.): Howell Code, ch. 10, 48 (1865). Arkansas: Ark. Stat., ch. 51, Art. IV, 5 (1858). California: 1 Cal. Gen. Laws, 1450, 48 (1865). Colorado (Terr.): Colo. Rev. Stat., ch. 22, 45, 46 (1868). Connecticut: Conn. Gen. Stat., Tit. 122, ch. 7, 124 (1866). Delaware: Del. Rev. Stat., ch. 131, 7 (1893). Florida: Fla. Rev. Stat., div. 5, 2614 (passed 1868) (1892). Georgia: Ga. Code 4286, 4287, 4290 (1867). Kingdom of Hawaii: Haw. Penal Code, ch. 13, 11 (1869). Illinois: Ill. Rev. Stat., div. 5, 49, 50 (1845). Kansas (Terr.): Kan. Stat., ch. 53, 7 (1855). Kentucky: 1 Ky. Rev. Stat., ch. 28, Art. IV, 11 (1860). Louisiana: La. Rev. Stat., Crimes and Offences, 5 (1856). Maine: Me. Rev. Stat., Tit. XII, ch. 160, 4 (1840). Maryland: 1 Md. Code, Art. 30, 201 (1860). Massachusetts: Mass. Gen. Stat., ch. 165, 18 (1860). Michigan: Mich. Rev. Stat., Tit. 30, ch. 158, 16 (1846). Minnesota: Minn. Stat., ch. 96, 13 (1859). Mississippi: Miss. Rev. Code, ch. 64, LII, Art. 238 (1857). Missouri: 1 Mo. Rev. Stat., ch. 50, Art. VIII, 7 (1856). Montana (Terr.): Mont. Acts, Resolutions, Memorials, Criminal Practice Acts, ch. IV, 44 (1866). Nebraska (Terr.): Neb. Rev. Stat., Crim. Code, ch. 4, 47 (1866). [478 U.S. 186, 194] Nevada (Terr.): Nev. Comp. Laws, 1861-1900, Crimes and Punishments, 45. New Hampshire: N. H. Laws, Act. of June 19, 1812, 5 (1815). New Jersey: N. J. Rev. Stat., Tit. 8, ch. 1, 9 (1847). New York: 3 N. Y. Rev. Stat., pt. 4, ch. 1, Tit. 5, 20 (5th ed. 1859). North Carolina: N.C. Rev. Code, ch. 34, 6 (1855). Oregon: Laws of Ore., Crimes - Against Morality, etc., ch. 7, 655 (1874). Pennsylvania: Act of Mar. 31, 1860, 32, Pub. L. 392, in 1 Digest of Statute Law of Pa. 1700-1903, p. 1011 (Purdon 1905). Rhode Island: R. I. Gen. Stat., ch. 232, 12 (1872). South Carolina: Act of 1712, in 2 Stat. at Large of S. C. 1682-1716, p. 493 (1837). Tennessee: Tenn. Code, ch. 8, Art. 1, 4843 (1858). Texas: Tex. Rev. Stat., Tit. 10, ch. 5, Art. 342 (1887) (passed 1860). Vermont: Acts and Laws of the State of Vt. (1779). Virginia: Va. Code, ch. 149, 12 (1868). West Virginia: W. Va. Code, ch. 149, 12 (1868). Wisconsin (Terr.): Wis. Stat. 14, p. 367 (1839).
For instance, Florida sodomy laws make cunnilungus illegal for both men and women. Therefore, no 14th Amendment violation.
In contrast, Texas sodomy laws make cunnilingus illegal for women only.
Florida sodomy law is constitutional, Texas sodomy law is not.