There is no such general requirement. However, passengers are forbidden from interfering with crewmember duties, per 91.11:
No person may assault, threaten, intimidate, or interfere with a crewmember in the performance of the crewmember's duties aboard an aircraft being operated.
So in practice a passenger is required to comply with many instructions, where failure to comply would interfere with the PIC's ability to fly safely.
"Stop talking because you are distracting me during a critical phase of flight" would likely be considered such an instruction. (Though the pilot may be better served by just turning off the intercom). "Stop slouching, bad posture offends me" would probably not be.
Note also that disobeying this law is not a crime. The FAA can levy civil penalties (e.g. fines) against passengers who ignore crewmember orders, but they can't send them to jail or anything. There is a criminal prohibition against physically interfering with crewmember duties in 49 CFR 46504:
An individual on an aircraft in the special aircraft jurisdiction of the United States who, by assaulting or intimidating a flight crew member or flight attendant of the aircraft, interferes with the performance of the duties of the member or attendant or lessens the ability of the member or attendant to perform those duties, or attempts or conspires to do such an act, shall be fined under title 18, imprisoned for not more than 20 years, or both. However, if a dangerous weapon is used in assaulting or intimidating the member or attendant, the individual shall be imprisoned for any term of years or for life.
But this does not apply to merely disobeying a instruction.