It's sometimes okay to ask people their age. If someone is young, like less than thirty, it's usually fine. Or if you know them. I don't usually ask 30+ year olds unless I know them, because some of them are sensitive about their age, but I wouldn't say it's very personal or a secret. I am willing to tell anyone who asks. 

That said, it's a little weird to ask a stranger. And it's true that sometimes when a man asks a young woman her age, it's because he wants to know if it's legal for him to have sex with her. But other times the person asking is just curious or trying to make small talk. If it makes you uncomfortable, you can say so. Most people will respect your boundaries, and you dont need to talk to the people who don't.