You quote seems to be from the ravings on this site: https://froudesociety.wordpress.com/2017/02/11/why-bapism-why-now/
'cuck' is a supposedly unfriendly monicker for everyone perceived to be 'self-confessed conservative - but really not' or something of the sort, it's etymology is muddled and full of weirdness. It mostly is used as an insult/touchstone.
'civ' in this context probably refers to 'civilized' in contrast to the 'barbarianism' that is espoused.
'civcuck' thereby is a meld of the two words above.
As neither conservative, civilized, barbarian, or actually any of the longer words employed are used in their usual meaning, the overall context as well as the specific word in question are extremely open to interpretation, which might be the intention.
For etymology of cuck: Source and popularity of the recent slang word "cuck"