The faction that the Nurgle cult would really hate is Tzeentch, which incidentally is probably the easiest faction to argue for being able to stay undetected and be hard to stomp out. Chaos Undivided in general won't have a beef with anyone unless it's a specific faction, and vice versa. And if all else fails you can always pull out the option
Ku'gath, also spelled Ku'Gath, and known as Ku'gath Plaguefather or just the "Plaguefather," is a unique Great Unclean One, a Greater Daemon of Nurgle, the Chaos God of disease and decay. Ku'gath is driven by an eternal quest to discover the most perfect pestilence that has ever existed. The corpulent and foul Great Unclean One known as Ku'gath began, humbly enough, as a diminutive Nurgling
Tzeentch will tank your authority, plus the tzeentch warshrine doesnt mimic festuses DOT. Belive it or not, tzeentch goes amazing with khorne, because of the fire damage, and doesnt reduce khorne authority. I did a vid on the nurgle slaanesh combo lastnight so just editing it so should go up today or tomorrow.
Tzeentch players: "man I hate Jeff so much, better fuck up his chances for promotion by learning everything about him and his weakness." That is why the chaos god 'rivalries' are Tzeentch-Nurgle and Slaanesh-Khorne, even though most people think it should be Tzeentch-Khorne because Khorne doesn't like magic. Khorne actually doesn't mind
General Tropes The Four Great Gods of Chaos: Khorne Tzeentch Nurgle Slaanesh Notable Daemons of the Chaos Gods Daemons of Khorne Daemons of Tzeentch Daemons of Nurgle Daemons of Slaanesh Daemons of Chaos Undivided
This is oppose to Tzeentch who represent "forced change", change that would occur because someone wanted it to. Regardless of outside elements. Nurgle is a scientist in the micro sense. He's constantly inventing newer, deadlier, more virulent, and more gruesome diseases.
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why does nurgle hate tzeentch