If I were to open the boiler before and after using it just as I have a wood stove, that brief exposure to trace amounts of toxins once a day would not influence a choice to use it. That theory is quite far fetched.

The finding that gas stove toxins can be significant is also more recent than the popularity drop in gas ovens. IOW, to have a cause-effect, the cause must come chronologically before the effect.

(edit) also worth noting that gas stoves are still popular in Belgium, just not ovens. So this theory is bogus. People are not going to avoid ovens out of fear of toxins when the door opens while at the same time having no problem with gas stoves.