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See Aruch HaShulchan YD 117:27 where he makes clear that people can rely on the kula to operate a store in which they sell some non-kosher products, since the majority of their business is with kosher things, and the only reason they are selling the non-kosher things also is because they would lose business if they didn't have these things available also. And that is talking about the owner of the store who profits directly from the sale. All the more so for an employee, who is not profiting directly from the sale (in most cases, unless he is on commission, which is unheard of in a food store), but rather is simply being paid for his time, in which case the whole din against sechora should not apply to the employee at all.

And, regarding basar b'chalev problems, in the Aruch HaShulchan 87:10, he allows even frying basar b'chalev in case of great financial need, since the prohibition of frying and roasting is only d'rabanan anyway. And he writes that this question is relevant to inns, where Jews would work and cook on behalf of their non-Jewish guests. So we see here even a leniency for short order chefs frying on a griddle or grilling on a BBQ to cook basar b'chalav, if their livelihood depended on it.

Therefore, the question does not get off the ground. For centuries Jews have worked as employees for non-Jewish businesses dealing in all manner of non-kosher products, and there is no suggestion whatsoever that an employee would be violating the prohibition on sechora. And as we see from the Aruch HaShulchan, most poskim have been exceedingly lenient even for the businesses owners themselves, since they understood that livelihood was at stake.

(However, to temper my original comments slightly: I did see that the Pischei Tshuva on YD 117:6 is strict about being a "shaliach" of a non-Jew to profit from forbidden things, but I assume that case is talking more about a commission relationship, as opposed to a standard hourly employee. Yabia Omer YD 4:6 discusses the entire question in great detail, about a Jew offered a job as a cook in a non-kosher restaurant, and comes out leniently in the end)

See Aruch HaShulchan YD 117:27 where he makes clear that people can rely on the kula to operate a store in which they sell some non-kosher products, since the majority of their business is with kosher things, and the only reason they are selling the non-kosher things also is because they would lose business if they didn't have these things available also. And that is talking about the owner of the store who profits directly from the sale. All the more so for an employee, who is not profiting directly from the sale (in most cases, unless he is on commission, which is unheard of in a food store), but rather is simply being paid for his time, in which case the whole din against sechora should not apply to the employee at all.

And, regarding basar b'chalev problems, in the Aruch HaShulchan 87:10, he allows even frying basar b'chalev in case of great financial need, since the prohibition of frying and roasting is only d'rabanan anyway. And he writes that this question is relevant to inns, where Jews would work and cook on behalf of their non-Jewish guests. So we see here even a leniency for short order chefs frying on a griddle or grilling on a BBQ to cook basar b'chalav, if their livelihood depended on it.

Therefore, the question does not get off the ground. For centuries Jews have worked as employees for non-Jewish businesses dealing in all manner of non-kosher products, and there is no suggestion whatsoever that an employee would be violating the prohibition on sechora. And as we see from the Aruch HaShulchan, most poskim have been exceedingly lenient even for the businesses owners themselves, since they understood that livelihood was at stake.

See Aruch HaShulchan YD 117:27 where he makes clear that people can rely on the kula to operate a store in which they sell some non-kosher products, since the majority of their business is with kosher things, and the only reason they are selling the non-kosher things also is because they would lose business if they didn't have these things available also. And that is talking about the owner of the store who profits directly from the sale. All the more so for an employee, who is not profiting directly from the sale (in most cases, unless he is on commission, which is unheard of in a food store), but rather is simply being paid for his time, in which case the whole din against sechora should not apply to the employee at all.

And, regarding basar b'chalev problems, in the Aruch HaShulchan 87:10, he allows even frying basar b'chalev in case of great financial need, since the prohibition of frying and roasting is only d'rabanan anyway. And he writes that this question is relevant to inns, where Jews would work and cook on behalf of their non-Jewish guests. So we see here even a leniency for short order chefs frying on a griddle or grilling on a BBQ to cook basar b'chalav, if their livelihood depended on it.

Therefore, the question does not get off the ground. For centuries Jews have worked as employees for non-Jewish businesses dealing in all manner of non-kosher products, and there is no suggestion whatsoever that an employee would be violating the prohibition on sechora. And as we see from the Aruch HaShulchan, most poskim have been exceedingly lenient even for the businesses owners themselves, since they understood that livelihood was at stake.

(However, to temper my original comments slightly: I did see that the Pischei Tshuva on YD 117:6 is strict about being a "shaliach" of a non-Jew to profit from forbidden things, but I assume that case is talking more about a commission relationship, as opposed to a standard hourly employee. Yabia Omer YD 4:6 discusses the entire question in great detail, about a Jew offered a job as a cook in a non-kosher restaurant, and comes out leniently in the end)

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See Aruch HaShulchan YD 117:27 where he makes clear that people can rely on the kula to operate a store in which they sell some non-kosher products, since the majority of their business is with kosher things, and the only reason they are selling the non-kosher things also is because they would lose business if they didn't have these things available also. And that is talking about the owner of the store who profits directly from the sale. All the more so for an employee, who is not profiting directly from the sale (in most cases, unless he is on commission, which is unheard of in a food store), but rather is simply being paid for his time, in which case the whole din against sechora should not apply to the employee at all.

And, regarding basar b'chalev problems, in the Aruch HaShulchan 87:10, he allows even frying basar b'chalev in case of great financial need, since the prohibition of frying and roasting is only d'rabanan anyway. And he writes that this question is relevant to inns, where Jews would work and cook on behalf of their non-Jewish guests. So we see here even a leniency for short order chefs frying on a griddle or grilling on a BBQ to cook basar b'chalav, if their livelihood depended on it.

Therefore, the question does not get off the ground. For centuries Jews have worked as employees for non-Jewish businesses dealing in all manner of non-kosher products, and there is no suggestion whatsoever that an employee would be violating the prohibition on sechora. And as we see from the Aruch HaShulchan, most poskim have been exceedingly lenient even for the businesses owners themselves, since they understood that livelihood was at stake.