If you are in a nuclear war, this may be the least of your problems, but you should indeed avoid hair conditioner.
According to this article, hair conditioner may act like a glue, holding in radioactive dust close to your head.
You should use shampoos designed to remove dust and not leave any goop behind.
Good luck with your next nuclear war, we hope this has been helpful for you.
Avoid using conditioner on your hair in event of nuclear war, know why