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In the sinusoids of the liver, venous blood from the hepatic portal system mixes with arterial blood from the hepatic arteries.
Do oxygen molecules move between oxygenated RBCs and non-oxygenated RBCs, so that the partial oxygen saturation of the blood in the sinusoids reflect partial saturation of the RBCs? Or do RBCs retain their initial oxygen saturation, so that the partial saturation of the blood in the sinusoids reflects a mixture of saturated and unsaturated RBCs?
The oxygen saturation (in lungs) and desaturation (in target organs) takes place via diffusion along the concentration gradient (i.e. partial pressure for gases). Therefore as long as RBCs from two different sources and having different partial pressure of oxygen mix up, the oxygen level starts to equilibrate between these cells.
But diffusion as a passive mechanism is not very fast and can take some time. So the only possibility for the second variant (there is a mixture of two types of RBCs) is if the mixture exists for very short time in liver sinusoids, so that the blood leaves them without really mixing completely up.
This is not true, at least in some animal models the blood within the liver seems to reach equilibrium very quickly and its resulting partial pressure can be influenced by adjusting the blood flow from different sources (using vasoactive substances injected directly, as in the referenced paper).
I'm not aware of any studies that investigate the equilibration of oxygen saturation between two individual cells in hepatic sinusoids, but I will answer based on what we know about these issues in the general context.
See West, Pulmonary Pathophysiology, Ch 2, oxygen loading in a healthy lung occurs to full saturation in about 0.25 seconds, one-third of the available contact time:
This involves diffusion through surfactant, the alveolar membrane of an alveolar cell, the cytoplasm of an alveolar cell, the basal membrane of an alveolar cell, the basal lamina, the basal membrane of an endothelial cell, the cytoplasm of an endothelial cell, the luminal membrane of an endothelial cell, plasma, and the membrane of an RBC. (see this illustration from Ross Histology)
In the liver, oxygen rich blood arrives from the hepatic artery, nutrient rich blood arrives from the portal vein. Blood from these different sources mix directly in the same vessel in the same hepatic sinusoid. There is no alveolar cell, basement membrane, or endothelial cell in the way. Oxygen just has to diffuse across one plasma membrane, in blood, and across another plasma membrane, all in a fluid moving together.
Diffusion of a small molecule like oxygen is quite fast, and RBCs are made for rapid diffusion, even of a large globular protein like hemoglobin.
