Rabbi Dr Dror Fixler published an interesting psak in the recent edition of the torah journal "Techumin" that is making some waves.

Rav Fixler basically paskened that one is allowed to eat freely in a vegan restaurant that does not have kashrut supervision. A person eating in such a restaurant should request that his food be prepared with no wine or vinegar. Fixler add that generally vegan restaurants are happy to show the kitchen to their customers so it would be good to ask to see the kitchen, if possible and look at what ingredients and items are being used in the process.

Machon Tzomet, the publisher of Techumin, added reservations to the discussion and recommend that anyone looking to rely on the psak in practice should read the article and psak in its entirety along with the various reservations before making a decision.
source: Kipa

I would point out this this is not really anything new. The issue has been under debate for a long time, with some rabbis paskening as Rabbi Fixler did and others paskening that one cannot just eat in a vegan restaurant without kashrut supervision.

In light of Rabbi Fixler's article, the Kosharot organization republished its article on why you cannot eat in a vegan restaurant without kashrut supervision. The issues they raise are largely the wine and vinegar, which Fixler addressed, along with issues such as infested greens, bishul akum, and sometimes other issues as well.

A Chabad rabbanit from India posted on Facebook (in a closed group, so it is not shareable) that Rabbi Fixler is wrong and she used her own experience in India as an example of how serious bug infestation can be and the problems it presents.

Worth noting is that INN brings a response from Chief Rabbi Rav Yitzchak Yosef who commented in his weekly shiur last night that the issue is complex and not one to be lenient so flippantly about. Rav Yosef goes on to criticize the rav for being lenient base don  logic without doing much research and without speaking to the gedolim about it. This actually bothers me because he probably has no idea how much or little research Rav Fixler did on the subject and I personally find it highly unlikely that he came up with a kula "klachar yad" - flippantly - and then published it in a respected torah journal without any actual research. I am sure he spent a lot of time researching the matter and Rav Yosef would have been better explaining why Rav Fixler is wrong, or why he disagrees, rather than saying he didnt do enough research.

I would add, and I am not sure it is 100% relevant but it seems to me to be connected, that, at least in the USA, it was common (and might still be?) for people to rely on a psak (not sure from who) that when necessary, such as for a business meeting that cannot be missed, one could eat a salad, sans onion, in a treif restaurant. It seems the same issues discussed above would apply - bugs in the greens, vinegar-based salad dressings, etc - yet no big deal was ever made of that. So perhaps in some places it is more of an issue, such as in India perhaps, while in other places it is less of an issue..

Anyways, as always, never rely on a general article no the Internet for psak halacha, but ask your rabbi if you find yourself in such a situation.