People don't have to use chemicals or synthetic fertilizers for growing tobacco. For example, organic farming is not a new issue for Turkish tobacco farmers, they always grow it this way since the tobacco plant arrived this lands. Bugs, caterpillars and etc. (pests) may eat the leaves or tobacco plants may not reach huge sizes. Is this what you want for tobacco ? It's not for me. Of course this is not a problem for cigarette tobacco growers, still tobacco will be shredded. But there're some organic solutions for pests for the good looking tobacco leaf growers (e.g. cigar wrappers). Do you think Cuba is using pesticides or synthetic fertilizers (which are mostly by-products of the iron-steel industry) on their valuable tobaccos, no.
Let the bugs eat some of the leaves, also they can't eat the whole crop. They may eat one (whole) plant out of twenty plants (by leaf weight). If you examine carefully some tobacco plants (for same strain) are more preferred by pests, others may be less preferred. So take seeds from the less preferred (by pests) plants, next year you may have more pest resistant plants.
For the fertilizers, you may prefer to use manure (cow, sheep, etc.). But if the animals don't eat organic plants their manure won't be organic. Today, nearly 80% of the cattles are fed by GMO corn so they have to get antibiotics to survive and there're antibiotic residues in their manure as well as their milk and meat.
But if you have your own cattles (or chickens, rabbits, pigeons etc.) and are feeding them with fresh or dried grass (or other natural herbal produts) you'll have organic fertilizers.