American here. Lived all over the country, many regions, small towns and big cities. Clarifying so our friends from Europe and Australia don't get the wrong idea.
It's not offensive to ask someone their ethnic heritage here. It's a fairly common topic of civilized discussion. I ask my white friends about theirs ("Irish and German" is a legitimate answer) and they ask about mine. I ask my brown friends and they ask about mine. I ask my friends of all colors and shapes and sizes (well, it's tough to have that conversation with African-Americans, simply because there's usually no way for them to know. America's great tragedy and national shame and all that). I can't remember a time when there's been any kind of hurt feelings or animosity as a result. These are perfectly lovely conversations. Sometimes they last 30 seconds, sometimes hours.
This is something that bugs me about Jeph's particular brand of wokeness: the assumption that if you can find a way to be insulted by something, you should. To be honest, Brun's matter-of-fact reaction to Peter's question about her ethnicity seemed totally legit. If she doesn't want to have an emotional stake in answering that question, then she doesn't have to. Sure, Peter's take on the issue of ethnicity (ie. "Tell me your heritage so I can get a boner over it") is reductive and depersonalizing, but that doesn't necessarily mean that curiosity about someone's genetic background is bad overall.
Look, using someone's racial heritage as a way to otherize them sucks. Don't do it. And if someone approaches it in that way ("Where are you from? No, but I mean where are you from? Tell me where you come from, strange one!") then you have every right to shut them down. But don't get so wrapped up in your fears of persecution that persecution becomes self-fulfilling. I play acoustic guitar and I like ultimate frisbee and part of my family is from Istanbul. These are all parts of me, and if someone wants to get to know me better, why would I get upset at them for it? I don't get mad when someone asks if I play a musical instrument or what sports I like, so why would I get mad when they ask about my family's history?
It's ok to be interested in people. It's ok to be curious about people. It's ok to be attracted to people. It's ok to ask about people. There is no set of things that are inherently wrong to be interested in or curious about or attracted to. Be polite, be kind, be understanding, and move forward.