Some characters for LS you won't be able to gain influence with them without shifting towards LS alignment as a DS PC. A character that would likely be hard would be Mira and Bao-Dur. However, darkside players get Hanharr as another different character.
As DS, characters that are easier to influence for darkside conversations would be Atton, Visas and Hanharr. Disciple can be influenced towards the darkside as well as Handmaiden, depending on your character's gender. With Disciple, you need to know which dialogue options with him trigger lightside points, and just select those that allow influence gains without incurring LS points.
Game was made this way so that characters respond differently. Some will agree and some will not.