In the RAQ you provided an answer about vaccine requirements for new hires. What about performers or presenters we hire to come into the library, especially to work with children? Are we allowed to ask/require proof of vaccination status before signing a contract?
A library needs two documents to address this issue:
2. Its current Safety Plan.
How does the contract/rider come into play? One of the conditions it should list is a "behavior requirement," requiring that any person performing a service at or for the library "will abide by the library's policies, and the reasonable requests of library staff."
How does the Safety Plan come into play? This is the document that likely addresses vaccination, PPE, and other safety requirements for those visiting your library.
Now, see how the two work together: the Safety Plan is a library policy; the "behavior requirement" means visitors must follow it.
When the two documents are assessed together, if it isn't crystal-clear that the library requires proof of vaccination before performance, the Safety Plan or the contract/riders--or both--can be amended to require:
To maximize the safety of in-person events, the ABC library requires all providers of in-person events to provide current proof of vaccination against COVID-19 at least seven days prior to the event.
The ABC library will consider remote options if a prospective performer or presenter requests such a change as a reasonable accommodation under the ADA due to a disability.
How can this be done so simply?
While there are many nuances that libraries must consider prior to flatly requiring vaccination for all employees, WHEN IT COMES TO CONTRACTORS PROVIDING ONE-TIME OR PERIODIC PERFORMANCES, unless there are grant requirements or other obligations specifically hemming a library in, a library can be more blunt in its requirements.
While they can be a very beloved part of a library's offerings, independent contractors have less rights than employees when it comes to a library imposing the conditions on performance. This is because, whether incorporated, or working "DBA", independent contractors are free to accept and reject the terms of any particular contract--and thus have more leverage and freedom than employees. And because of that, when it comes to requiring them to provide proof of vaccination, there are a few less legal hoops to jump through than with employees (new, or otherwise).
So, after all that, what were the questions? "What about performers or presenters we hire to come into the library, especially to work with children? Are we allowed to ask/require proof of vaccination status before signing a contract?"
The answer is: with the right policy and contract terms in place: yes.
 A document you can attach to the performer's contract or proposal, setting the terms of the work.
 There are any number of forms a standard contract or "rider " for a library to engage performers and presenters can take. It can be in the form of a friendly letter that outlines the terms of the arrangement, or it can be a more formal document that sounds like it was written by a lawyer. Either option is OK, so long as it addresses the fundamental questions: what is being done, how much the person is being paid to do it, and what rules and expectations protect the library from any risks related to the performance. For comments on contracts for performers (both generally and in the COVID Times), dive back into history and review the "Ask the Lawyer" at https://www.wnylrc.org/ask-the-lawyer/raqs/125.
 Very standard stuff.
 Which at this point (August 2021) you have probably amended at least five times.
 Because contracts with providers of more essential/routine services such as delivery, cleaning, and security are likely to be more complex, this guidance does not apply to those types of services...although of course a library can explore amending a contract with such a provider to require maximum allowable safety measures.
 That's the theory, anyway.
 A library should work with a lawyer to have a stock performance contract tailored to that library's identity, insurance coverage, and other unique factors.