@SunsetSeeker Chilchack specifically explains during the discussion of payment on p25 that he has to stick with the job because he took his pay in advance. It's pretty well established that Chilchack is a stickler for his brand of professionalism, and that this sometimes commits him to trouble he'd sooner avoid.
As for Care, you'd have to care more than is strictly sane to stick with Laius. Consider the conditions of his mission:
To descend further into the dungeon than almost any other party (again).
To do the above without the supplies or funds that enabled the first descent.
This, with no prospect of affordable and trusted hires to replace party losses.
To manage the rigors of descent with a single spellcaster pulling double duty as mage and healer, constrained by her limited mana.
To defeat, at half- or two-thirds strength, a dragon that wiped a full-strength party.
To do all the above at greatest possible speed (and therefore least possible caution), risking exhaustion or special attention from the wildlife in their haste.
This, at the risk of dying deeper in the dungeon than any resurrectionist dares to go.
All signs point to a suicide mission, above and beyond anything Namari has likely done in the course of making a living. It's unreasonable to compare concern for colleagues' well-being with willingness to risk permanent, irreversible death. Less so to determine that the presence of the first but not the second indicates shallowness or hypocrisy. Caring comes in degrees.