For writing proofs, full knowledge of English is not necessary. Most proofs can be written using a single tense. It is sufficient (and often advisable) to keep the structure of sentences very simple; that is very similar to how logic statements are written using math notation. Arguably, this exercise requires students to use only a small and simple subset of English level. Most students are expected to have it by the admission requirements of the course they signed on.

Your experience resonates with me. In my classes I also have many students with imperfect English. I have often noticed (including as recently as a couple of weeks ago) that when I give lengthy word questions explaining a complicated real-life problem and asking to model it mathematically, some students struggle to understand what they are being asked to do due to language difficulties; and this is despite the fact that the question is written in grammatically correct, plain English, and I even make a conscious effort to edit the questions and “water down” the level of the English by removing complicated words and phrases to the extent possible.

Although I haven’t gotten pushback and don’t believe I have anything to answer for, thinking about this issue over the years has led me to conclude that there is a real problem of students who come to US universities with an incomplete mastery of English being at a disadvantage — often a significant one — because of their language skills. And I’ve wondered what I can do about it. For example, consciously trying to speak and write with slightly less complicated English words and phrases than I might be inclined to do if I knew I was addressing only native English speakers is one remedy. But it is a small and mostly (as far as I can tell) ineffective one. The students who were going to struggle are still struggling.

Now, whether or not this is “unfair” is a complicated ethical question and I don’t think it is my place to answer it. But one thing I’ve come to believe is that, at least, to the extent that it is unfair, the unfairness is a systemic kind of unfairness that is built into a university system that admits a large number of foreign students and expects them to handle an environment in which knowledge of (high-level, academic) English is assumed. In other words, it is not me who introduced the unfairness, and it is not me who has much power to do anything about it.

At the end of the day, my job is to teach mathematics, using English as the language of instruction, and that is what I do. If the subject I’m teaching involves writing word problems to teach people how to model and interpret real-life problems, that is what I will do. If the subject requires students to write proofs verbally, that is what I will require (though grading will be done based on the mathematical correctness of the answer and not based on correct grammar and spelling). There just isn’t any other way.

When a student says to you that what you are doing is unfair, tell them that you are simply teaching the subject you were assigned to teach as it should be taught by a qualified instructor. Ask them what they are suggesting that you do instead. My guess is they will not be able to make a coherent suggestion, and perhaps that will lead them to understand that the problem is more complicated than they realized.

Also: tell the advisors at your college not to tell students that mathematics does not require strong language skills! That is a horribly false and misleading thing to tell people and can obviously set them up for trouble and disappointment.

Being at a disadvantage due to a lack of necessary skills does not seem unfair to me. The ability to communicate clearly in written form is an essential skill for pretty well everything that we hope that our students will go on to do in their later life. Thus, it is a skill that we should actively encourage them to develop, by pretty much the same methods that we encourage them to develop, say, mathematical skills. That includes methods such as assessing them on that ability.

Just for reference, my department explicitly awards 20% of the available marks on each assignment (not including exams, because expecting people to re-draft work under time pressure is unreasonable) for "clarity of written communication". Neither this, nor a more implicit approach, is unfair: it is an assessment system rewarding better results to more able students, which is precisely what assessment systems are supposed to do.