Conservative ignorance of the law is exceeded only by their hate and stupidity.
Denying an injunction does not mean the plaintiffs have 'lost' anything.
The order is procedural, having nothing to do with the merits of the families' case, where the order is based on the type of documents provided, not the fact that the children are indeed US citizens:
“In his ruling denying an emergency order sought by families, Judge Robert L. Pitman of the U.S. District Court for the Western District of Texas in San Antonio said Texas officials can refuse to accept
matricula consularcards, issued by Mexican consulates, as a form of identification to obtain birth certificates for U.S.-born children.”
Judge: Texas can deny birth certificates for U.S.-born children of some immigrants
The judge is also aware of the fact that Texas is likely acting in bad faith, where the state's concern is not with the 'integrity' of their issuing process, but an unwarranted hostility toward immigrants and their US citizen children:
'Although Pitman noted the families’ attorneys had “provided evidence which raises grave concerns regarding the treatment of citizen children born to immigrant parents,” he said the court needed more evidence before issuing the emergency injunction they had sought.'
ibid
Once acceptable documentation is provided, or the state's requirement is invalidated by the courts, the US citizen children will be issued their birth certificates.