Most of the websites and apps nowadays are keeping our data unless they're telling truthfully that they don't record logs. If there are still websites that don't take your details and erasing it as soon as you're done with them, they're likely a few of them.
Except being closed-sources, do you have some examples of "red flags" I can spot easily? Do you have some clues to be sure that a service is probably not good?
Think of each of them that you should be careful of, even if there are no red flags as long as you're into their premises and platforms, the possibility is high of recording every move you do on them and every detail you input.