Final answer:
A rigid membrane would not support the idea that the ancestral eukaryote was a predator cell because it inhibits flexible movement and engulfing capabilities necessary for consuming other cells.
Step-by-step explanation:
The characteristic of an ancestral eukaryote that would not support the idea that it was a predator cell capturing and consuming other cells is a rigid membrane. A predator cell requires flexibility to engulf prey through processes like phagocytosis. A dynamic cytoskeleton, large cell size, and the ability to move are all traits that would support the predatory nature of a cell, as they denote an active and adaptable organism capable of chasing and consuming prey. On the other hand, a rigid membrane would inhibit the flexibility needed for engulfing or surrounding other cells, which is crucial for a predatory lifestyle. Therefore, the presence of a rigid membrane (d) does not align with characteristics anticipated in a predatory ancestral eukaryote.