They mean the same thing but feel different. "I may not do this" is a simple statement of fact. "I do" is a SUBJECT + VERB combination. That is the most important grammatical construction in the English language. It is the way we express action. It is decisive. It accomplishes something. "Doing" is a present participle behaving as an adjective. It is not a verb. It can accomplish no action. It has no subject (though it has an object, "this"). Acting as an adjective, it describes the subject of the sentence, "I". "I am doing this" does not state that anything gets done. It is only a description. You can think of "I am doing this" as a photograph of yourself doing "this". Saying "I am doing this" is the same as showing someone that photograph and saying "this photograph describes me".

The first one is simply redundant and may even be incorrect. You’re saying you’re in the process of not doing something. I mean that is implied when you’re not doing something. Or you say you’re not gonna be able to so xyz until a certain day, then the listener knows you are in the active process or not. doing that certain task. Why not say “I won’t get to it until Tuesday” or “ I may not be able to do this until Tuesday” or “I don’t think I’ll be able to do this until Tuesday”. There’s many ways of saying this very succinctly and casually. Like I always say don’t make it too complicated.

The difference between "I may not be doing this until Tuesday" and "I may not do this until Tuesday" lies in their focus on the action and its ongoing nature. "I may not be doing this until Tuesday": This sentence suggests that the action is ongoing or continuous, and there's a possibility that it won't be completed until Tuesday. It implies that the action is currently in progress or planned to be started, and there's uncertainty about its continuation until Tuesday. "I may not do this until Tuesday": This sentence suggests that the action itself might not occur until Tuesday. It doesn't specify whether the action is ongoing or not at the moment. It simply implies that there's a possibility that the action won't happen until Tuesday. In summary, the first sentence emphasizes the ongoing nature of the action, whereas the second one focuses more on the timing of the action without specifying its ongoing status.