You are not required to be a
Chick to have all five LIs as options.
Neutral works, too. If you just keep a balance between the
Chick and
DIK major choices, you'll be locked into the
Neutral affinity when you eventually get to the Flush Papers decision. Here's an example of the choices that will keep you on track with all the LIs (from my main playthrough):
View attachment 1754890
Of course, there are many combinations. As long as you don't sway too far on either end of the scale by the time you get to the Fake ID decision, you can stay
Neutral.
The choices you make outside of the major decisions have a far greater impact on which LIs are available as options, anyway. Yes, the game will present you with certain alternative actions, dialogues, and scenes depending on your affinity, but your affinity will affect the availability of side girls more than LIs.