The Hindu ambassador would be bound as is any other US ambassador regarding what they should and should not be doing with regards to their professional agendas. See below.
The Chief of Mission -- with the title of Ambassador, Minister, or Charg? d'Affaires -- and the Deputy Chief of Mission head the mission's "country team" of U.S. Government personnel. Responsibilities of Chiefs of Mission at post also include:
•Speaking with one voice to others on U.S. policy--and ensuring mission staff do likewise--while providing to the President and Secretary of State expert guidance and frank counsel;
•Directing and coordinating all executive branch offices and personnel (except for those under the command of a U.S. area military commander, under another chief of mission, or on the staff of an international organization);
•Cooperating with the U.S. legislative and judicial branches so that U.S. foreign policy goals are advanced; security is maintained; and executive, legislative, and judicial responsibilities are carried out;
•Reviewing communications to or from mission elements;
•Taking direct responsibility for the security of the mission -- including security from terrorism -- and protecting all U.S. Government personnel on official duty (other than those personnel under the command of a U.S. area military commander) and their dependents;
•Carefully using mission resources through regular reviews of programs, personnel, and funding levels;
•Reshaping the mission to serve American interests and values and to ensure that all executive branch agencies attached to the mission do likewise; and
•Serving Americans with professional excellence, the highest standards of ethical conduct, and diplomatic discretion.
). I don't really think Americans are losing sleep over cultural face of the DR, let's be realistic. Agreed, that he should be more culturally sensitive, that s what he is paid for.
