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The Torah commands us not to cause or even help a fellow Jew to sin. Therefore, someone observant is not permitted to lend anything to someone non-observant if it will be used to desecrate Shabbat. For example, an observant Jew may not lend a car to a non-observant Jew over Shabbat.
An observant Jew may invite a non-observant Jew to come for the Friday night meal unless one offers the guest the option of staying for all of the Shabbat. This is the case even if one knows the guest will almost certainly choose to drive home after dinner. As long as the host honestly offers the guest a place to sleep, the guest’s acceptance of the invitation does not have to involve desecrating Shabbat.
Some do not allow a synagogue to host a bar mitzva for a non-observant family when it is clear some of the guests will drive to the synagogue on Shabbat. Others permit it on the grounds that the synagogue members are not asking anyone to drive, and if those guests were not driving to the bar mitzva, they would be driving somewhere else. In practice, as long as the non-observant guests are respectful of the synagogue and make sure not to desecrate Shabbat there (such as by using their phones), the synagogue may host the bar mitzva. Another alternative is for the family to have the boy called up to the Torah on a Monday or Thursday rather than on Shabbat.
