What is "taytottlers"?

Conrad means the word "teetotaler", someone who doesn't drink alcohol:

teetotalism: the principle or practice of complete abstinence from alcoholic drinks

Almost all the dialogue in Conrad's short novel is written in a way that emulates the accents of the men speaking. As a result you can't assume any words are correctly spelled, but sometimes have to guess what the word should be.

As ben says, since the character of "Belfast" is presumably from Belfast, if you were to write out the way someone with that Irish accent sounds when speaking the word "teetotalers", "taytotallers" is probably pretty close.