There are two ways to receive citizenship at birth: via the 14th Amendment and the Common Law precept of jus soli; or via statute (primarily limited to jus sanguinis, though also under some circumstances to non-genetic biological relationships).
This law applies equally to everyone, regardless of whether they are straight or gay.
Of course, certain assumptions that can be made for marriages between a man and a woman, such the presumption that the husband is the father of the wife’s child, can not made between same-sex couples who are legally wed to each other because granting that assumption would require that we presume the biologically impossible. Thus, a child born to someone in a same-sex marriage could never be born within the wedlock of the legally wed couple.
When the Supreme Court overturned prohibitions on “same sex marriage”, it was declared that same-sex and opposite-sex marriages are equivalent and that any potential inequivalencies were just “irrational animus”.
Mother nature is clearly, then, an irrational hate-filled b***h.
That citizenship, by statute, generally grants citizenship by birth to natural (i.e. genetic) parents (and non-genetic children carried by a surrogate U.S. National mother, in some cases), seems to fly above the head of a writer at The Daily Beast. Even the headline (“Trump Administration to LGBT Couples: Your ‘Out of Wedlock’ Kids Aren’t Citizens”) and chaser (“Children of U.S. citizens are falling victim to a policy that de-recognizes their parents’ marriage—and strips them of their birthright citizenship.”) are fundamentally dishonest or written out of ignorance.
In all the examples provided, there is no indication that the same rules would not apply to opposite-sex couples in the same actual situation, or to single individuals. There is no “de-recogniz[ing]” of any legal marriage.
The first example is of two men legally marriage to each other who went to Canada and used a surrogate and an egg donor to conceive a child. It was not explicitly stated that either of the men’s sperm was used, but for the sake of argument such assumption is granted. In an identical situation, a man and a woman, who claim parentage of a child born of a foreign surrogate with an extra-marital egg donor, would be in a similar situation. The child would be born out of wedlock and in accordance with the law—8 USC 1409(a)—the father would need to demonstrate a blood relationship. This is the same exact situation as with the two men aforementioned.
Oh, one might muse, an opposite sex couple could just not mention the child was born through surrogacy using an extra-marital egg donor, and their parentage would be assumed, and that it is “irrational animus” that stops same-sex parents from doing the same. Of course, one would then have to irrationally assume with animus the biologically impossible. That opposite sex couples could more easily get way with it is a function of basic biological possibility.