What kind of responsibility has a Gentile to Jews who are not observant? For example, a Gentile sends a text message to his non-observant Jewish friend, knowing that he will most probably write a message back on the sabbath; or the Gentile offering non-kosher food to a non-observant Jew who will probably accept his offer. Providing of course that the Gentile is aware that his behavior will cause the breaking of a mitzvah on the side of the Jew, is he also to be held co-responsible in any grade for the violation?
Gentiles are not obligated in the mitzvot besides the Seven Mitzvot of B'nei Noach. According to Tosafot on masechet Avodah Zarah (15b), the prohibition of "placing a stumbling-block before the blind" is not one of those seven commandments, so technically, a gentile is not responsible for a non-observant Jew's actions.
The simple reading of the gemara and the opinion of some other Rishonim, however, is that the particular prohibition of "placing a stumbling-block" is a derivative of each individual commandment. As such, causing someone to murder (for example) is a part of the same exact prohibition as murder itself. Therefore, lifnei iver applies to gentiles as well as Jews for all prohibitions that apply to them (even when the person they cause to transgress is also a gentile). Still, since gentiles are not obligated in shabbos, the lifnei iver prohibition with respect to shabbos wouldn't apply to them.
Nonetheless, it is a major halachic problem (for the Jew himself) to knowingly violate the commandments, so it would certainly be appropriate for a non-Jew to go above the letter of the law and refrain from causing a Jew to willingly violate halacha. While he may not be punished for not doing so, I would imagine he would be rewarded in the world to come for the extra effort.