Why doesn't it matter which nonradioactive isotope of oxygen you breathe?

Because they all have the same chemical properties and can be used for breathing.

Explanation:

Conceptually, isotopes are atoms that have the same number of protons, that is, they are distinct species of the same element, differing only in the number of masses and neutrons.

Oxygen is a colorless, odorless and tasteless gas, poorly soluble in water, present in nature as three stable isotopes: oxygen 16 (present in 99.75% of occurrences in the environment); oxygen 17 (0.37% of occurrences) and oxygen 18 (0.20% of occurrences). All forms of non-radioactive isotope of oxygen can be breathed by living beings, because they all use the same kind of chemical properties, so all have the same function.

they it depends on if one believes about radioactivity, they make a geiger counter beep but maybe it was going to beep anyway electronics do wierd things all the time or it was programmed to beep near certain metals.