Usually these two topics are not joined but in this case they follow the same warning.
For most of China it is hard to communicate and even if you ask, and the question seems to be answered fairly clearly, you should take caution.
For example, many times we have tried to help vegetarians and tell the server, the server will then take our order and some of the food clearly has meat in it.
We can usually tell and since the price is low, it is fine to just not eat the obvious food. The explanation from a Chinese friend was that the dish was a vegetable dish (even though it had meat in it) so that is why it was still server to us. There is also the fact that educated people rarely work in the restaurant industry in China especially if you are paying hardly anything for the meal.
If you have a Chinese person with you (that speaks English) that knows the dishes they can definitely help.
You can also try to remember some common dishes and order them more.
In the larger cities there are more fancy restaurants that cater to vegetarians or vegans, but the price is generally much higher than any local simple restaurants.
Chinese people also have allergies and I think allergies may be taken more seriously than being a vegetarian or vegan, but still it would be a mistake in China (and anywhere for that matter) to just mention something to the server and hope it isn’t lost in translation.