Is it unreasonable to ask a photographer not to share photos on social media?

False. Plenty of case law protecting photographer's copyright regardless of them being paid or not. I do stills and video photography and it boils down to this. If I'm pushing the shutter release: my gear, it's my copyright; your gear, it's still my copyright unless the contract states otherwise. If I'm providing the gear, I absolutely won't sign a WFH contract that releases my copyrights, and I've had clients try to use standard contracts to sneak WFH in. If the client is providing the gear, then it's generally understood to be WFH and the contract spells that out, like on a film set where contracts and copyrights are very strict. You're absolutely right that the safest step is to get everything in writing. A contract should protect both parties.

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