Conversation

Fun fact about the replicators
They're based on transporter technology, specifically molecular materialisation. This allows them to take the raw undifferentiated matter in the ship's storage and materialise it into the requested pattern.

What's in the matter storage? Well the molecular materialisation also works in reverse, so uneaten food, cutlery etc good back into the replicator. But also, the ship recycles all waste.
So, yes. The crew is eating reconstituted poop.