Q. In the above case or when people who are not religious are invited to a Shabbat meal, will non-mevushal wine become prohibited?

A. Bais Yosef (Y.D. 119) quotes Rashbo’s Responsa that considers the wine of one who openly desecrates Shabbos as prohibited Gentile wine. This is, at least in principle, the accepted common Halachic rule. Chasam Sofer (Y.D. 120) explains that this is not an assimilation preventive measure but rather a penalty imposed on a recalcitrant mumar.
However, contemporary Poskim express also lenient opinions on today’s unobservant individuals as they may be considered the unwitting victims of prevalent ignorance and society or media compulsive preassures. (Binyan Tzion 23, Mahari Assad Y.D. 3, Sheilas Yavetz 60, et.al.)
Considering also other mitigating Halachic issues, such as what kind of “negia” or contact with the wine prohibits, or what portion of the wine is affected, Horav Shlomo Miller’s Shlit”a opinion is to be lenient in need for the purpose of kiruv or sholom bais.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a