Another poster also added another key thing: record every interaction on this topic (and advise them at the outset you are doing this), and get everything in writing.

If it is not in writing, it does not exist, for the purposes of the law (and speaking generally).

Also require them to justify their position by requiring them to produce all of the documents used to create the requirement, any precedent-creating examples of how they made an experimental medical treatment mandatory, clearly define what will happen if you refuse, etc.

HR will most likely go talk to Legal, absolutely PANIC when Legal tells them what is about to happen to them if they proceed, and then return back to you and cancel the mandate.