It will have an impact but not much. If it is a criminal record, it must be 100% affected. Public security detention is an illegal record, not a criminal record. Moreover, public institutions are not government agencies. Only when applying for the national civil service, enlisting in the army, or taking the military academy exam, will they be more strict.
Similar influences also exist in the recruitment of government institutions. Although there is no clear stipulation that those who have such circumstances cannot be admitted, it will still have some impact in actual operation. Under the same conditions, they must be admitted on the basis of merit. If you apply for a public security civil servant, if your parents, uncles and other direct relatives are serving a real sentence, you can't pass the political trial.
Legal basis
Article 26 of the Civil Servant Law of the People's Republic of China:
(1) Having received criminal punishment for a crime;
(2) Being expelled from the Communist Party of China;
(3) Being dismissed from public office;
(4) Listed as the object of joint punishment for dishonesty according to law;
(5) There are other circumstances under which employment as a civil servant is prohibited by law.