How to know a red wine is Kashrut?

Are you Jewish? If not, your wine doesn't have to be kosher anyway.

If you are Jewish, you should know that no one who takes kashrut seriously would drink wine without a hechsher. Any wine you choose outside of the little kosher section at the liquor store isn't kosher. You can justify ignoring the halacha however you like--plenty of people do. BUT...

The most important thing to know here, since you don't know about wine, is that you shouldn't serve non-hechshered wine to people who keep kosher. And if you're not a Shabbat-observant Jew yourself (and this means 'Shabbat-observant' according to halacha and 'Jewish' according to halacha, not in accordance with your own interpretation), you shouldn't serve them non-mevushal kosher wine, either, if you've opened it or handled it after it's opened.

/r/Judaism Thread