Many of us now use dash cams; to record what happens outside of the car, and what happens inside of the car. A dash cam is a useful tool to help protect us drivers from false claims or to provide video to an insurance company after an accident.
Rideshare companies are happy for drivers to install cameras, but urge drivers to check local laws to determine what 'consent' is required.
Some states have a "single party consent" system, which essentially means that only one party to a conversation needs to give consent for electronic recording to be considered lawful. As a driver, you are a party to the conversations in your car, and can therefore give consent to record.
However, there is ambiguity as to whether the 'single party consent' provides coverage to record video, or just audio (see this useful pdf).
To overcome this, I have applied these stickers to the doors of my car, which lets the passenger know very clearly that they will be recorded.
If the passenger feels strongly about being recorded, I explain that the video is not kept, and that it offers both myself and the passenger some protection. If they still feel strongly, I invite them to cancel the ride and arrange for a new driver to pick them up. Fortunately, most passengers do not seem to mind the recording - in fact, they appreciate the fact that drivers are vulnerable to the poor decisions of some of our passengers.