The question is general,[1] and the answer follows suit. For the purpose of this halachic investigation, we are referring to a case in which one can assume that the customers are not Jewish.
It is permitted to benefit from most non-kosher foods. Some notable exceptions are chametz, wine with a concern of use for idolatry, and beef and milk that were cooked together. In such cases, one may not earn money from dealing with them, even if he does not own the food or derive direct physical benefit from it.[2] However, it is uncommon for these foods to be forbidden in benefit according to all opinions. Regarding wine, many are lenient about benefit in times (like ours) when libations for idolatry are rare,[3] and many meat and milk combinations are permitted in benefit (e.g., poultry, meat from a non-kosher animal, and when the combination took place without cooking[4]). It is thus possible that one could work in a non-Jewish restaurant without violating a prohibition of benefiting from forbidden foods.[5]
Another issue is working professionally with food that it is forbidden to eat.[6] The gemara[7] derives that even concerning forbidden foods from which one may benefit, one may not seek to obtain them for commercial purposes (sechora), but he can sell that which came his way unintentionally. According to most Rishonim,[8] this is a Torah-level law, although significant opinions among Rishonim and Acharonim maintain it is Rabbinic.[9]
The Rashba[10] says that the prohibition’s rationale is that one who does commerce with food might eat it. Indeed, the prohibition concerning animals applies only to those non-kosher animals, dead or alive, which one has that are slated for eating (e.g., pigs, as opposed to horses). However, most poskim[11] posit that the prohibition applies even if a specific owner of the right type of animal is not in a position in which it is feasible that he will eat its meat.
Your question relates to the opposite case – someone who does not own the food but is in a position in which he is liable to eat it. The Pitchei Teshuva[12] assumes that if the prohibition of sechora is intended to distance one from eating the food, we should follow that logic for stringency and not allow one to work with non-kosher food, even if he does not own it. However, many poskim[13] do not extend the prohibition to include such a worker.
There are often additional grounds for leniency in certain situations. Sechora is prohibited only regarding food forbidden by Torah law.[14] In many dairy eateries, the food is primarily forbidden Rabbinically, at least according to many opinions (further discussion is beyond our scope). When the commerce is mainly not the type to which the prohibition of sechora applies, then despite the fact that some of the commercial activity is problematic, it is likely not forbidden. A classic example pertains to one who raises animals for their kosher meat; he is allowed to sell the forbidden parts of the animals to non-Jews.[15] We see from this that when most of a worker’s activity revolves around food that it is permitted to deal with commercially, the fact that he will have a small amount of activity with foods that are forbidden based even on Torah law should not present a problem.
Even when the prohibition of sechora does not apply, however, it might still be halachically required to refrain from situations in which one could easily come to eat non-kosher food.[16] One interesting source is the Maharsha,[17] who discusses a situation in which one separates the non-kosher part from the kosher part of an animal and then cooks both (not together) before selling the former to non-Jews. The practical concern of eating the non-kosher food may be influenced greatly by the type of contact one has with the food and the extent to which he has permission to eat freely from the food with which he is working.[18]
In cases of great need, some poskim were reluctantly lenient and allowed people to work in non-kosher settings. However, the severity of the issues and the level of need vary greatly (e.g., a nurse in a non-kosher hospital vs. a waiter in a non-kosher restaurant), and each instance requires the specific ruling of a rav.