Do any birth certificates show the parents birth dates?

No, a birth certificate is about the child, not the parents. Only the parents names will appear, nothing else.

No just their age

No, a birth certificate is about the child, not the parents. Only the parents names will appear, nothing else.

No just their age

I worked for social security for 32 years as a claims rep in the US; I've seen (literally) thousands of birth certificate and have never seen the parent's birth dates on one single birth certificate. Usually, though, the long-form birth certificate would show the age of the mother at the time of the birth or, at least they used to, don't know about now. I have never seen a birth certificate, short-form or long-form, which showed the dates of births of the parents - never.

And of course if an age is given, it isn't necessarily right - people often lie or the person providing the information doesn't know and guesses.

Not in any country I know of. But of course I don't know about all of them. In any case, it would only be what the parents told the registrar, so you couldn't rely on it.

Not from any country I know they don't, but it is secondary information anyway, so can't be trusted even if they did, same with death certs which several countries civil death certs show the persons birth date, again you can't trust it as it is 'given' information from someone who was not present at the time of the birth, so is guessing/assuming/giving informatioon they think is correct.

EG my grandmother was the informant on her mother death cert, giving date of birth and also instructed the mason on dates on her grave stone when I researched and found all the records of my great grandmothers, only two records gave the same date of birth, her birth cert and baptism record ( both primary record) each and every census she gave a different age, her marriage cert a different age....she married someone 25yrs older than she was and so said she was older than she was, reality is she died aged 62yrs, her grave and death cert say she was 83yrs old