Of course people just starting their careers shouldn't ask their parents for career advice — it's very unlikely they have relevant, current knowledge and much more likely they'll draw from 20+ year old info that worked for them.
That said, parents are great for doing a "smell test" on an email, a resume, on an outfit, or on anything really. Hiring managers are likely to be closer to parents' age, so it's good to get feedback. Parents are also going to have much stronger professional networks that can help even if you're in an entirely different field — colleagues' spouses might work in the right industry, or someone else might have a good connection. Just a small example that happened to me recently — my daughter was on a group trip that was getting screwed by their hotel, and one of the parent chaperones happened to be an ex-VP of a credit card company, and could make a call to the right person to get the problem resolved.
In short, think carefully about how people can help you and have an open mind about things they might know or connections they might have — you might be surprised.