This is not about free speech. It is perfectly acceptable for an organization to offer guidance and perhaps impose restrictions on how their own employees portray a topic publically in the name of PR and hopefully even compassion for their human audience. In other words the government can agree not to use certain words in public communications. This is very different from policing the general public when say talking about the CDC. That would be unconstitutional.

Do I agree with this personally? I dont know. It's probably better to offer a style guide for reasons other comments have already covered.