Fundamentally and ethically, it seems quite unfair that the consumer is the one who gets the short end of the stick with regards to being informed about the contents of their wine, especially in North America where laws for keeping potentially harmful ingredients out of this beverage tend to be less stringent.
GMO yeasts meet with legal approval in North America
If you're concerned with GMOs in the products you are consuming you may need to be careful with which wine you are drinking.
Back in 2014, GMO yeast ML01 (a yeast which helps large corporations to speed up the fermentation process) for the first time was approved and added into wine in North America where GMO's are unregulated. The EU has banned this practice, as wine yeasts are unstable and genetically altering them can lead to unforeseen toxicity in the final product. Even though the FDA has declared it GRAS (generally regarded as safe), no independent studies have been conducted outside of the company who developed it for further safety assurance.
Expounding on this issue is that yeasts are wild and ambient and can easily cause unsolicited contamination in neighboring vineyards who are vehemently against their use. This is a risky practice and one that can have devastating effects, similar to the way that the use of Roundup has contaminated unsuspecting neighbors working in the agricultural sector.
How do you know if your wine contains GMO yeasts? Your best bet is to buy wines outside of North America, buy organic wines (some will even have the Non-GMO Verified certification) or solicit the winemaker and hope they are honest with you.