Before you refuse, it's worth understanding what exactly this requirement means. Sometimes contracts say one thing, but in practice they mean something completely different - for example, the camera needs to be technically ready to turn on, not literally streaming all day. Ask for clarification: do you need to stream constantly or is it enough that you're available for video calls? Some companies are fine just seeing your status in the system and being able to call you anytime. But if they really do require non-stop video without breaks - that's a whole different story.
As for privacy: the law on this is pretty murky, it all depends on the country and the specifics. But practically speaking, it means your employer will see your home, your surroundings, even intimate moments. Plus constant surveillance tanks your concentration and drains you psychologically. People perform worse when they're being watched like they're in prison rather than when they're judged by results.
Here's concrete advice: ask them in writing to agree on a compromise - for example, camera on only during meetings, or only during certain hours, or you turn it on on demand within five minutes. Make your pitch not something like "it's inconvenient for me," but a practical argument: "This will optimize bandwidth and let me work more productively." If your employer won't budge, that really is a red flag.