Acc. to most opinions, Non- Cooked wine can not be touched by a Jew who is not Shommer Shabbos. I am not clear as to the reason. The main reason, nowadays, given for Stam Yainom is not to intermarry. This is clearly evident on Daf 57 B, Tos. "Leafukai ", at the end, explaining why the Prohibition of Stam Yainom is only drinking, and not receiving Benefit. There the Tos. clearly compares the prohibition of Stam Yainom to Beishul Acum. The Pitchai Teshuva, Y.D. , Siman 113 : 1, writes that the prohibition of Bishul Acum does not apply to Non -Religious Jews, since there is no prohibition of marrying their daughters, since they are Jewish ( quoting the Teferet Moshe ), and even if you want to say , that there is a prohibition of Bishul Acum , because the Non-Religous Jew might cook you Non-Kosher food ( Bies Yosef ), This reason does not apply to Wine. The fact that the Non-Religous Jew touches your bottle of wine ( ie. at you Shabbos table or Seder on Pesach ) , will not render the ingredients of the wine Non-Kosher. ??
The Ran in Chulin (4b) writes that although there is no Chashash of "B'noseihen" (since they are Jewish), nevertheless since a Mumar has the status of a Nochri, he is included in the Gezeirah of Stam Yayin. See also Chasam Sofer (YD 120).
If this is true, than the prohibition of " Beshul Acum ", would also apply to non religious Jews. And this could lead to a major problem going to restaurants and food stands in Israel, where there are many non religious Jews ?
See the attached Teshuvah from the Tzitz Eliezer who quotes several Teshuvos who wish to compare the two Halachos. However, he concludes based on the Chasam Sofer and Rav Shlomo Kluger that although a Mumar is like a Nochri as far as wine is concerned, this does not apply to Bishul Akum.