A context, for the purposes of your question regarding Othello, would mean the situation in which the play is seen or read, the time, place, and circumstances. For example, Othello is often read by high school students and discussed in the classroom. That is one context in which it is "received." Another context would be the play put on at the Globe Theater in England, during the time that Shakespeare was alive, some time after approximately 1603, when it was written. Still other contexts would be a run of the play in the rural South of the United States in 1935 or a performance in 2015 in Brazil. This play has been read or performed in many different contexts since it was written over 400 years ago.
I would say that for the most part, Othello has been well-received in its various contexts, with some exceptions that are worthy of note. It has many themes that transcend time and place, such as trust, love, ambition, betrayal, and jealousy. These are all themes that are universal, and audiences respond to such themes because they can identify with them. However, it has some themes that some audiences find abhorrent, for example, a mixed race love and marriage, adultery, and fairly frank discussion of sex. There are no doubt parents who would find it objectionable for their children to read or see such a play. There are places where these themes are the subject of great disapproval, as they were likely to have been in days past in the rural South or even, perhaps, today. Every context reflects the society in which the play is received. So a society that frowns upon mixed race marriage, for instance, is likely to frown upon a play that deals with this subject. A society that feels strongly about adultery might very well disapprove of a play about even a hint of it. I would say, though, that in today's world, the play, read or played to most audiences, is likely to be well-received because of its universality.