[tag:united-states]

> Given a workplace IT system which is necessary to complete one's job
> duties, what rights, if any, do you retain as an employee to withhold
> your consent?

Essentially none, unless you personally, or your union, negotiated a contractual term for your employment that provides otherwise.

You have essentially no legal rights to privacy from your employer about what you are doing while you are on the job.

> Sub-question: by extension, could an employer require an employee to
> consent/agree to a physical search?

There are jobs, such as working in a mint (i.e. a manufacturing facility for coins), working in gold or diamond mines, working in factories that manufacture controlled substances, working in advanced biotech labs, working in secret national security facilities, and working in prisons and jails, where this is common. As a practical matter of employee satisfaction and finding a way to hire new employees, it isn't very common where the need to do so isn't obvious, but it isn't legally prohibited. 

IT monitoring is particularly common in the finance industry to discourage embezzlement and other forms of financial fraud. I have a relative who works in the back office of a bank who is required to take a complete two week vacation with no remote work every year to allow auditors to review their computer files and work in a context where the employee doesn't have any ability to interfere.

Law enforcement officers, meanwhile, are frequently required to wear body cameras on the job.

Truckers and delivery people often have GPS systems that report back to headquarters to monitor their every move and speed at all times. Bus drivers often have this monitoring and also constant security cam and dash cam monitoring.