Boy, I'm real hesitant to go to HR. May as well ask to be fired.

It really depends on the business, culture, climate. The better places I've worked, this kind of interest is genuine, an attempt to foster better relationships at work. Of course, some people are just nosey Nellies...

Without knowing the environment and culture (and the questions), it's hard to say what to do.

Best I can say is to make it clear you like to keep your work and private life well separated.

Also OP, if someone else feels insulted, that's on them. They've chosen to feel insulted. Besides, how do you know she feels insulted? If she's communicating that, then she's being manipulative, using "emotional blackmail". Look, I'm not responsible for how you choose to feel, that's on you.

One trick I've used with people who continue with questions is to respond with a non-sequiter, something jarring, and use it all the time, repeatedly. Something like "how about the weather", or "how about those ". Make it your catch phrase for when people continue to pry, and don't be afraid to repeat it. Keep in mind tone matters, so say it like you mean it, like you walked in on Monday after a team did well, or got their asses beat. You don't even have to like the sport or the team, in fact it's kind of funny if you don't like them.

It's a bit of re-framing the conversation, while also communicating you aren't interested in the subject, without being an ass. And if anyone complains, well, you were just talking about a sports team.