Are academic associations obliged to comply with the US government?
The organizations you mention, while not controlled by the US government, still need to obey all applicable laws and regulations; employment laws, for example. 

But the government, sometimes by presidential decree, has wide latitude to set regulations related to national security. In many cases the claims don't actually need to be proven. That is the nature of "national security". The fear is that it may be too late if you have to wait for congress to act or for solid proof. 

Whether this is good or not is a long standing debate as the power can be abused.