Privacy.
Also, traditionally, hosts go out of their way to help their guests feel welcome, not the other way around.
> People should be free to share (or not share) their personal information any way they please.
"Privacy" is about so much more than "personal information". Heck, it is irrelevant whether the conversation contains "personal information".
It is also very clearly not only the hosts who are affected here.
> Is being "open-minded" about other people's choices in this regard so much to ask?
It can be when that implies collateral damage on your side.