I actually do think this behavior (as described) is somewhat discriminatory (not intending any legal claims) and if this happened in the department where I am DGS I would put a stop to it. However, I can't guarantee that academic authority figures would be this reasonable in general. Basically as I see it your (again, self-described) language abilities are being policed on the basis of your ethnicity, independent of facts that should establish you as a native speaker beyond doubt. I think you are right to be upset by it.
However, I agree with fuzzylogician that you sound very upset in your writing, and I would try to eliminate all trace of emotion in your communication with authority figures; this may well be impacting your speaking/writing ability independent of native language. _If_ your chair is somewhat sympathetic and you haven't already done this, you should convey in a neutral calm fashion that you believe this is happening on the basis of your ethnicity and nothing else. The wording in an email might be something like as follows, which I've attempted to make unemotional but still strongly worded: "I'm perplexed at the situation and don't know what to do. I grew up in the US, went to a US high school, and a US university, and am a native speaker of English. As a linguist in training, I think I have some confidence in what this entails. The only reason I can see that I would be singled out as an alleged L2 speaker is my ethnicity." If you use the term ESL instead, I would expand it rather than use the acronym out so that the phrase "second language" is visible. I don't know that this is a battle you will win, unfortunately, because the chair may have to play unpleasant politics if they are inclined to do something, and may not perceive it as worth it for an MA student they don't know (harsh, but possible). If you have a DGS in your department, you could try them first, this would be more following the academic "chain of command".
You should also be aware going forward that there are studies showing that students in classroom settings with Asian teachers (and probably other visible non-white ethnicities, but I've only seen studies with Asian teachers) show strong unconscious biases in their evaluation of accents regardless of the objective presence of these accents. So I'm guessing you are Asian (or hispanic for an outside chance) because this sort of racism is not unknown.