Asking questions from a place of curiosity (as opposed to from a place of judgement) isn’t invasive.
How can we ever get to know people and grow relationships if we can’t ask questions?
If you’re a safe person to me, I am reasonably sure there aren’t any questions you can’t ask. (If you’re not, that’s another story entirely.)
Poking around in people’s brains is one of my favorite past times—though it’s been missing-ish in my recent years of too much to do and not enough socializing—and I am grateful to people who don’t keep walls up to prevent it.
When in doubt, avoid questions about hot-button topics, but really, any question (or comment) can be a button-pusher for the right person. We can’t possibly know what are sensitive subjects for people, especially if we don’t know them very well. “What made you move to Arizona?” is a pretty common question around here, but if the person you’re talking to was escaping an abusive situation, that question is a lot more emotional than someone who just wanted a change. No way to know unless you ask.
We get to know people through talking to them. (Sometimes simply through spending time with them, but there are a lot of asterisks on that.)
Academically, I learned in grad school a process that probably has a formal name but basically deals with self-disclosure. In order for two people to form a positive emotional relationship (not limited to romantic relationships), mutual self-disclosure is required.
One person needs to disclose something about themselves at a level appropriate to the depth of the relationship, the disclosure needs to be met positively, and the process needs to repeat in reciprocity.
The whole process isn’t exactly a tit-for-tat, one-to-one series of interactions, but the relationship quickly becomes imbalanced if only one person is doing the disclosing, or if one’s disclosures are substantially deeper than the other’s.
So. Reveal yourself. Ask questions. Answer questions. Build connections. At the end of the day, those connections are where our fulfillment is.