Automation in the life science research laboratory is a paradigm that has gained increasing relevance in recent years. Current robotic solutions often have a limited scope, which reduces their acceptance and prevents the realization of complex workflows. The transport and manipulation of laboratory supplies with a robot is a particular case where this limitation manifests. In this paper, we deduce a taxonomy of biolaboratory liquid containers that clarifies the need for a flexible grasping solution. Using the taxonomy as a guideline, we design fingers for a parallel robotic gripper which are developed with a monolithic dual-extrusion 3D print that integrates rigid and soft materials to optimize gripping properties. We design fine-tuned fingertips that provide stable grasps of the containers in question. A simple actuation system and a low weight are maintained by adopting a passive compliant mechanism. The ability to resist chemicals and high temperatures and the integration with a tool exchange system render the fingers usable for daily laboratory use and complex workflows. We present the task suitability of the fingers in experiments that show the wide range of vessels that can be handled as well as their tolerance against displacements and their grasp stability.