So far I haven't used a Campden tablet, but my experience of brewing is limited as I only started last October!
First up was the riskiest of all (according to what I have read) a wild yeast, home-pressed apple cider. Maybe I was lucky, but it worked. I probably will sulfite the starting-with-whole-apples cider this autumn as I plan on making several gallons, and I do think I was lucky last year. Incidentally, we also bottled fresh apple juice last year, the materials we used were clean but not sterile, we sterilised by pastuerising and adding a little vitamin C, it kept fresh for a couple of months until it was finished. We had one bottle (out of 30) where the seal on the bottle failed or it hadn't reached the proper temp and it spoiled.
A regular brew since then (about a gallon a fortnight, 6 gallons on the go at the moment!) is turbo cider from supermarket apple juice (and either sugar or fruit syrup). Using bought juice and fermenting dry there's no need to sulphite either at the start or the end as long as the equipment is sterilised.
Also on the go is 2 gallons elderberry wine (surplus homemade elderberry cordial plus supermarket grape juice) and 1 gallon of plum wine (homegrown frozen plums, sugar and water). Neither has required sulphite so far, but neither is close to being ready for drinking yet.
There are several ways to kill any nasties depending on the raw materials, plus good hygiene of materials (I do use chemicals to sterilise everything), good technique and you should be able to minimise the need for chemicals.