If a secular (non-observant) Jew touches wine that isn't mevushal does that render it not kosher for him to drink?
Nafka Mina: gifting non-mevushal wine to a secular friend.
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See J. David Bleich's article "May a Sabbath-Desecrator Drink Wine?"
There are a group of discussions that state that a mechalel shabbos befarhesia (deliberate transgressor of shabbos) will make the wine that he touches yayin nesech.
For example, see the answers to this question
Once that is done (since he is still a Jew), it would be forbidden for him to drink. This is similar to serving non-Kosher food to a "secular" Jew who does not keep kosher. The halachos of "tinok shenishba" (captured infant literally) may apply if he does not know the halachos of shabbos.
Note that even though the "stam yainam" takkana is made to prevent intermarriage (originally), once it was made, it must be kept in all circumstances. Thus, when a Jew is to be treated as a non-Jew (in certain cases), he is still forbidden to sin as a Jew. Thus a Jew whose wine is treated as if he were a non-Jew, would also be forbidden to drink it himself.
However, in the case that you specify, while the wine is mutar before you give it to him, his opening it could cause it to become yayin nesech and asur. As a result, you could be liable for "lifnei iver" (do not put a stumbling block before a blind person) by enabling him to sin.
As a result, you should only give your secular friend yayin mevushal.