Drop the scorn quotes. For those of us not just in the US, but anywhere in the Anglosphere, it is conservative to uphold "the privilege of the writ of habeas corpus," a part of the Anglo-Saxon legal tradition so venerable and well-established that the American Founders specifically mentioned it in the Constitution, and limited the Federal government's power to suspend it.
Whether Justice Barrett has taken the correct stance turns on whether you really think the Venezuelan and Salvadoran gang activity is really analogous to the Confederate secession and resulting hostilities, the armed take over of several counties by the KKK during Reconstruction, the Moro rebellion when the Philippines were a US territory, or the attack on Pearl Harbor (in the wake of which habeas corpus was briefly suspended in Hawaii). As an American conservative, I do not think the diffuse activities, albeit violent, sometimes horrifically so, of criminal gangs from Latin America justifies the suspension of the writ. Let anyone file a habeas corpus petition and challenge their deportation. If they are found to be in the country illegally, send them back to their country of origin. It may be slower, but one cannot make America great again, by getting rid of one of the things that made America great in the first place: fealty to the Anglosaxon legal tradition.