Can non-ordinary college graduates take the open recruitment examination of public institutions?

Yes, but there are few requirements. Specifically, you should look at the recruitment announcement and the requirements of specific positions. For example, some unsatisfactory units, such as urban management, can apply for the exam with their academic qualifications no matter what college they graduate from. The important thing is to review more and read more books. If you can apply for the exam, you must seize it, because there are not many opportunities for recruitment.