uh. I just started a new game as the Dark Urge and one of my goals is save all the tieflings this time. Should I give up this game and create a new character if I want to do that?
No need, you can save them all... but;
there is one particular Dark Urge scene you will have to entirely metagame in order to avoid it, which includes a particular female Tiefling. This scene with her always happens somewhere between Wyll's and Karlach's recruitment, so always save your game just before you decide to end the day and DO NOT recruit Scratch until after a certain female Tiefling visits your camp.
When she visits simply reload the save prior to long-resting and go knock her out in the Grove with a companion you don't care losing attitude with, could also just use a mercenary too. Then take a long rest and continue the awesome Dark Urge story.