There's a huge difference between 'sterilize' and 'disinfect' or 'sanitize'. Sterilize will kill everything if done correctly. The others just 'sanitize'---- but it's still better than not doing anything.
For people who can't use bleach (or just don't like the smell) they might try hydrogen peroxide.
Disinfect a Sponge
Of course that would take a lot of H2O2 and could be cost prohibitive and it still just 'disinfects/sanitizes'.
Some sources will say hydrogen peroxide and common white vinegar.
Cooks Illustrated and America's Test Kitchen said that the best way to disinfect (not sterilize) a kitchen sponge is to boil it for 5 minutes.
Microwaving was also good but there's a warning about sponges maybe catching on fire in them so I won't try that.
The Best Way to Clean a Sponge Cook's Illustrated | Apartment Therapy
Bleaching a sponge with sterilize
it--- but the use of bleach is avoided by many people, including me.
I don't know about putting them in the dishwasher. I haven't check on that yet but I do run mine through the washer every now and then.