There are a variety of synonyms that can be used in place of the phrase "be accepted". For example, one could say that their application was approved, authorized or sanctioned. Similarly, one might use the words acknowledged, endorsed or validated to convey the same idea. Other synonyms might include welcomed, embraced, or recognized. The specific word choice might depend on the context or tone of the conversation, but all of these words convey the sense that something or someone has been approved or recognized as acceptable.