I'm no expert on pharmacy in early twentieth-century Mexico, but my guess is that it was closer to the practice of previous centuries than to modern pharmacy, which was developing in Europe and North American at just that time. There was a clear distinction, historically, between a "droguero" and a "boticario", who had increasingly come to be known as a "farmacéutico" over the course of the nineteenth-century. The former, a "droguero", was essentially a tradesman who sold pharmaceutical ingredients, known as "simples", nearly all of them derived from plants. These were "drogas", crude drugs or raw materials. The latter, a "boticario/farmacéutico", was qualified to make up medicinal recipes, known as "compuestos": concoctions. This art was known as "compounding".

Now, the English equivalent of a "droguero" was a druggist. The confusion arises from the fact that this word is still used in American English to mean a pharmacist, but in the historical context, which was almost certainly still that of your text, they were not the same thing. So when it says "farmacéutico-droguista", these are not synonyms. It means he was both a skilled professional trained in the art of making up medicinal recipes (farmacéutico) and a tradesman who sold drugs (droguista).

"Droguista" is a synonym of "droguero", though the original meaning of "droguista" was a liar or cheat. As a term for a druggist it seems to have been used particularly in Latin American Spanish.

In English, exactly the same distinction used to apply. A druggist used to be strictly a person who sold drugs, pharmaceutical simples, as distinct from an apothecary, later called a pharmacist, who made up medicinal recipes. Dr Johnson defines "druggist" like this in the mid-eighteenth century: "one who sells physical drugs", the latter being "an ingredient used in physick; a medicinal simple".
http://archive.org/stream/dictionaryofengl01johnuoft#page/n6...

And the 1913 Webster dictionary defines druggist as follows:

"One who deals in drugs; especially, one who buys and sells drugs without compounding them; also, a pharmaceutist or apothecary. The same person often carries on the business of the druggist and the apothecary."
http://machaut.uchicago.edu/?resource=Webster's&word=druggis...

As we can see, the same was happening in English as in Spanish: the distinction was becoming blurred, and the term "druggist", like "droguero", was coming to be applied to a pharmacist, as it is today. Nevertheless, in historical contexts, the correct translation of "droguero" (or "droguista" in this sense) is "druggist", nothing else.

(It so happens that I co-authored a article on historical pharmacy involving a droguero, whom I called a druggist in the English abstract. Here it is if anyone is interested:
http://asclepio.revistas.csic.es/index.php/asclepio/article/... . This is just to assure you that I have studied this subject.)