This myth is alive and well apparently.
A no-rinse sanitizer can be made with bleach:
5 gallons water
Add 1oz distilled vinegar (5%)
Stir and then add 1oz bleach (around 8%)
The amount of chlorine is low enough that it does not need to be rinsed and will not cause off-flavors. Follow the links provided by
@jtratcliff.
The procedure isn't as stringent as
@Robert65 suggests, but it should be used in a well-ventilated area to avoid the possibility of inhaling chlorine gas.
"Impossible" is too strong of a word, but yes, you absolutely should use some kind of sanitizer rather than creating problems for yourself.
Bread yeast absolutely will make beer. Its attenuation will be similar to beer yeast and its alcohol tolerance is over 10% ABV.
Heat is arguably more effective than chemical sanitizers.