In order to avoid situations of mixed-marriages , which almost certainly lead to assimilation , the Rabbis enacted many decrees whose goal was to inhibit the forming of close relationships between Jews and non-Jews. The laws of stam yeinam (wine that was produced or handled by Non-Jews) are included in these decrees. On the other hand, the Torah, and in its footsteps, the Rabbis, wanted to encourage close relationships amongst Jews, and they therefore established that a single witness is believed regarding prohibitions. The Yerushalmi explains that this was done in order to enable Jews to conveniently eat and drink with their fellow Jews.
Let us therefore preface our response with some of the principles and basic laws regarding wine and when a non-Jew comes in contact with it, only afterwards will we deal with the issue of wine that comes in contact with a Jew.
Even if a non-Jew opens a bottle of wine, the contents are not prohibited . If a non-Jew pours a cup of wine, according to many opinions, the wine is prohibited , while some opinions are lenient if a monetary loss, even a small one, is involved . There is also a dispute regarding the permissibility of the wine that remains in the bottle . Even those who are stringent will permit the wine if a large loss would otherwise be incurred .
All this is regarding natural wine, but cooked wine was never included in the prohibition . There is a dispute amongst contemporary Rabbis if the pasteurization process renders the wine as cooked or not , one can be lenient, since this is a doubt on a rabbinic prohibition.
Now we will explain the law regarding wine that was poured by a non-religious Jew .
If he would open a bottle of wine, the wine is certainly permitted, as was mentioned earlier regarding a non-Jew, all the more so when it is opened by a Jew. If a non-religious Jew pours a cup of wine , if he is the type of Jew who does not fulfill the ritual commandments (bein adam LaMakom), since that is how he was educated and raised from a young age , then the wine does not become prohibited by his pouring or his touch.
However, if he declares about himself that he willingly is a non-believer as the result of his investigations and searches , and he publically violates Shabbat, meaning he violates Shabbat even in front of a great person , then he is considered as someone who is a heretic on the entire Torah , and the wine would be prohibited.
In any case where there is a doubt as to his status, one may be lenient, as is the case with every doubt on a rabbinic prohibition.
A full response in Hebrew with sources can be found Bemareh Habazak volume 7 siman 62:
http://eretzhemdah.org/data/uploadedfiles/ebooks/36-sfile.pdf