You can hand wash them in a bucket with washboard (though we didn't) and line dry them. We actually line dried ours about once a month to air them out and sun-bleach the cloth. About 30 $5-15 cloth diapers lasts you 3-4 days between washes.
Honestly, there is an epidemic of self defeatist in our day and age.
But damn, finding used diapers in the toilet is annoying. Plus wet diapers hanging all over to dry. If it's your kid, though, it's not a big deal.
Mold thrives in moist, dark places, not most sunny ones.
Also the society functioned differently; one middle-class salary could sustain a middle-class family, for one.
We no longer live in that reality, nor would anyone want to.
It's like saying that homeless people are OK because there were no buildings in prehistoric times.
Edit - and having lived in both, you're much better off drying things in a hot humid place than in colder ones.