The thing is, anyone who says 'I was born' was born in the past. So they say 'was'. But there's no reason we can't use all the other tense/aspect/mood forms about other people:
(1) My baby will be born next week, the doctor says.
(2) If my baby is born next week, I'll go home the week after.
(3) If my baby had been born a week earlier, I wouldn't have met you.
Now, while the baby is actually being born, coming out of the mother, we'd say 'is being born' because this is an action in progress.
So 'is born' is slightly restricted in use. But it can be used more or less anywhere you would use other verbs in the present tense. For example, it can indicate future under 'if', as in (2); similarly your 'when' example, where it's conditional but with no particular time. It can be used for something that has just this moment happened: A Star is Born. It can be used for habitual actions: Every child is born a poet.
You can use a synonymous phrase to understand it better. Say, come to life.
I came to life (was born) in 1951 - past simple
If your child comes to life (is born) with a health problem - present simple
Every child comes to life (is born) needing love - present simple
A star comes to life (is born) - present simple.
I don't agree with Ezgi Revontuli and Zio Gilito: A star is born doesn't make a general statement, it describes an ongoing event.