What anti-realist believe or say is beyond me. You're best listening to people more versed in what they actually say. They sound unhinged but that's only my opinion based on the snippets in this thread.I'm talking in the more general sense of any property whatsoever. To my understanding the "anti-realist" position says that the quantum system has no properties whatsoever, in the general sense. My interpretation is that the alternative to this is to say that the system does have some [unquantified] properties. My understanding is that to say the system has unquantified properties would be to say that it has hidden variables and is realistic.
So, the axioms of QM actually provide a means of being clear about "properties." I read property as an observable. An observable is an operator which has a spectrum, a set of allowed values that may be observed. This spectrum is unchanging and I would call it a property.
Now, upon measurement only one of the spectrum set is obtained as a result. This result is the property-value.