Describe how Othello is both accepted and rejected in Venetian society.

Othello is clearly respected as a soldier by the leaders of Venice. When several islands controlled by Venice seem likely to be under attack by the Ottoman Turks, the senate of the city sends for Othello. One senator refers to him as the "valiant Moor" and seeks his help in driving off the Turks. When the leaders of the city-state discover that he has married Desdemona without Brabantio's permission, they give him a fair hearing, and they eventually side with him once Desdemona informs them that she married Othello of her own volition.
At the same time, there is evidence of racial hostility against Othello, who is black. Sometimes this even takes the form of slurs, such as when Rodrigo calls him "thick lips," and Iago refers to him as an "old black ram" who is "tupping," or having sex with, Desdemona, a "white ewe." Brabantio's objections to their marriage are fundamentally rooted in race. So Othello's race makes him the subject of scorn and ultimately plays a role in Iago's scheming and the tragic end that befalls his marriage to Desdemona.
https://www.bl.uk/shakespeare/articles/racism-misogyny-and-motiveless-malignity-in-othello

Despite the fact that he is black and discriminated against, Othello's skill as a general has helped him achieve a high rank in Venetian society. He is referred to by the Duke of Venice as "Valiant Othello," and when Venice faces attack by the Ottomans, it is to Othello that they immediately turn. Othello describes to the council how Brabantio "loved" him, and "oft invited [him]" to his home, eager to hear stories of Othello's life. Desdemona falls for Othello because of his artistry in telling these stories, and the Duke of Venice opines that "I think this tale would win my daughter too."
However, Brabantio's behavior makes very clear to the audience that, while he is happy to respect Othello as a general and to entertain him in his home, the idea that Othello should marry Brabantio's own daughter is anathema to him. He can accept Othello as a soldier, but not as a son-in-law. Iago preys upon this prejudice in Brabantio when he calls from beneath his window that "an old black ram is tupping your white ewe." Elsewhere in the story, the racial epithets applied to Othello by Iago and Roderigo reveal the underlying prejudice of those who should otherwise have viewed him with respect. Othello is described in terms specific to his race, such as "the thick-lips." This suggests unhappiness at Othello not only for having won such a high position, but for having won it while being "other."