Is Manager of Local union allowed to disclose Disabilities or past medical info

[union worker24]

What is the name of your state (only U.S. law)? Florida

Recently the membership of my local union have been told by the Manager and Agent that before they will refer you to a contractor for work. The individual must have a doctors release because of past medical history.This is all pre-hire at the union hall before referral to contractor.
Is the Manager or agent allowed to disclose past medical history with contractors or workers comp claims before referral?
This is on an individual basis and not all of membership is required to do this.
The individuals involved have not filed any workers comp claims on anyone in past.Is the contractors allowed to ask about disabilities or medical issues before referral from the Agent or manager? Our union membership has allowed a 100% call by name and is now affecting the older members and those with a disability.