[Skooz]

...most notably the Texas Republican Party, who in their recent convention declared America a "Christian nation".

Such a declaration is in no way a violation of the First Amendment. Also, in no way was the Texas Republican Party advocating a Church of the USA or any other "state religion."

[Long Cut]

Perhaps not. However, it gives pause to those of other religions who might otherwise support the Party, and incidentally gives fresh ammunition to our Leftist adversaries in their drive to paint us all as "religious extremists" and "theocrats". In any case, it is reckless demagoguery, and arrogant besides.