Tyson is right to do this. Tyson is also within its rights to do this. Note that those are two separate things.
Tyson is also within its rights to mandate vaccines because a private property owner should be and is able to decide who enters their property. That goes to the core of what it means to own property - the right to exclude others. Here, Tyson is deciding they will exclude people who, by virtue of their poor medical decisions, pose a danger to others. Similar logic applies to decisions about who a private company chooses to employ.
It is almost comical how the supposedly "pro-liberty" people who oppose vaccines try and perform mental gymnastics to dodge the conclusions in the above paragraph. So, if any Tyson employee doesn't like the vaccine mandate they can go work somewhere else, as they have no right to set foot on Tyson's property.