Is it okay to use three-eighths PEX pipe for a tankless water heater manifold system?

It depends on the length of the run. 3/8 pipe tends to be a little small and will restrict the flow. Use the 1/2 if you can. It's not that much extra but it will give you much better water delivery. Of course, between the manifold and the water heater, use 3/4 inch or larger copper.

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I would have to agree with the previous contributor. 1/2" PEX is indeed the preferred size for running the water to the Plumbing fixtures.