How wise is it...to ask one..to PROVE what they choose to believe in?

If you have hope in your child and I ask you to prove it what would you say?

Asking for what evidence that supports a belief is a perfectly reasonable request. I want evidence that injections of disinfectant and exposing my internal organs to light is an effective treatment for Covid-19 before I shoot up Clorox and stick a light bulb up my butt.

Belief is never a choice, it is an outcome.

It is only worth asking a person about their beliefs if:

1/ it interferes with others.

2/ if it is interfering with their own life and that person is seeking help... as often they do.

Generally one is only asked that if they are expecting others to believe it as well.

not very wise. They sound like mathematical logic dorks. 

Many people ask that others believe it too. That's when anyone should ask how they know it to be true.

In the grand scheme it doesn't matter. They can choose to discuss their beliefs with you or not to. I never hurts to ask. but remember that no one owes you an answer to personal questions.

It certainly is when they threaten you to do the same or else.

You want to force your religion on everyone, you BETTER be able to prove it,  And you can't, you whine about faith, which is failure.  Why do you brag about failure, as if it is a virtue.  Faith is no virtue.  Myers said it best:

"FAITH. No one word personifies the absolute worst and most wicked properties of religion better than that. Faith is mind-rot. It’s the poison that destroys critical thinking, undermines evidence, and leads people into lives dedicated to absurdity. It’s a parasite regarded as a virtue." -- PZ Myers 

No one will ask unless someone is trying to get others to believe it.

Very wise if they are suggesting that others believe it. 

If they are not asking? I see no harm in asking because if you really believe in what  you do then you should be able to explain why you believe it and it should hold up to scrutiny depending on the manner and intention in which the question is asked.