Why is concealed carry allowed given I have a right to know who around me has a gun?

There is no body of law that says you have any such right, so the premise is false.

 Until after the Civil War, most places discouraged concealed carry, but encouraged open carry, under that general principle (but, importantly, they did not specify that the public had a ‘right to know’, only that, culturally, people who concealed were assumed to have done so for nefarious purposes).

With the rise of gun control laws originating in the South, carry of any kind became illegal, and so, of course, open carry disappeared, and that mindset has generally prevailed until today.