I hope the controversy is around any potential legislation on gas stoves, and not around a link between the mining, transportation, and burning of natural gas (read methane) and climate change...
Burning methane does not produce carbon monoxide if oxygen is abundant. A well-designed stove will burn it to water and carbon dioxide, which is harmless. AOC's family most probably used a bad stove when she was young.
In absence of oxygen, it's why direct heaters have been phased out in the US and still kills many in 3rd world countries (though to a lesser degree since monoxide safeties have been implemented). A stove can choke out a household especially tightly constructed one (as many new ones in N. America for energy efficiency reasons). Typically not a huge deal as the stove is only used for a few hrs at most. Monoxide poisoning or simply asphyxia will of course cause brain damage from lack of oxygen to the brain though I'm fairly certain monoxide is toxic beyond just causing hypoxia. Formaldehyde is also another byproduct of combusting hydrocarbons though I'd be surprised if it's dangerous levels w/NG.