The Smithsonian is not in the Executive branch. Trump has no authority there. But that won't stop them from complying and destroying their own museums.
> The Smithsonian Institution is a trust instrumentality of the United States ... Congress delegated the authority and responsibilities of the United States to the Smithsonian Board of Regents. ... The Smithsonian Institution is considered unique in the Federal establishment. The Smithsonian is not an executive branch agency and does not exercise regulatory powers, except over its own buildings and grounds. ... Thus, courts have held that the Smithsonian is not an agency or authority of the Government...