The phrase "be oblivious to" means to be unaware or ignorant of something. There are several synonyms that can be used instead of this phrase, such as "be clueless about," "overlook," "not notice," "fail to perceive," "ignore," "not familiar with," and "not mindful of." These synonyms can be used in different contexts to convey the same idea of being unaware of something. For example, instead of saying "They were oblivious to the fact that the store was closing soon," you could say "They were clueless about the store's closing time" or "They overlooked the store's closing announcement." Choosing the right synonym depends on the context and the tone of the sentence.