The Shulchan Aruch (512:1) rules that one may not invite a gentile to one's home for a Yom Tov meal. Although Halacha allows cooking on Yom Tov, one may cook on Yom Tov only for Jews; it is forbidden to cook food on Yom Tov for gentiles. The Sages therefore forbade inviting a gentile to one's home for a Yom Tov meal, as he might then prepare food for him in violation of Halacha.
The Mishna Berura (commentary to the Shulchan Aruch by Rabbi Yisrael Meir Kagan, the "Chafetz Chayim," Lithuania, 1835-1933) comments that a "Mechalel Shabbat Be'farhesya," meaning, a Jew who publicly and flagrantly violates Shabbat, has the status of a gentile with respect to this Halacha. Therefore, it would be forbidden to cook for a Shabbat violator on Yom Tov or even to invite a Shabbat violator into one's home.
However, Chacham Bentzion Abba Shaul (Jerusalem, 1924-1998) distinguishes in this regard between a Jew who knowingly violates Shabbat, and a Jew considered a "Tinok She'nishba," meaning, who was not trained in Halacha observance. Regarding this kind of Shabbat violator, who was raised in a secular home and a secular society that disregards the authority of Halacha, not only is one permitted to invite such a Jew for a Yom Tov meal, it would be a Mitzva to do so, as he thereby exposing him to the experience of Yom Tov celebration. Even if it can be assumed that he will come to the meal by car, it is nevertheless permissible and commendable to invite a Shabbat violator of this kind to one's Yom Tov meal. With regard, however, to a Jew who received a proper Torah education and nevertheless disregards the Shabbat prohibitions, it is forbidden to invite him to one's Yom Tov meal, even if he would arrive by foot, rather than by car.
Summary: One may not invite to his Yom Tov meal a gentile or a willful Shabbat violator who was trained in Halacha observance and knowingly rejected it, even if he will arrive by foot. It is, however, permissible and even encouraged to invite to one's Yom Tov meal a Jew who does not observe Shabbat because he did not receive a proper Torah education, even if it can be assumed that he will arrive to the meal by car.
