It’s not a taboo whatsoever or anything people don’t like to discuss.

It’s not something you need to discuss with your supervisor though as it’s simly not your business. You aren’t his friend. My friends would ask me questions like that and it’s perfectly fine. Not a taboo at all. You aren’t friends though. The difference in your and your co worker question that co worker was talking about him and his kids, you wanted to know about someone else’s kids :ex wife’s or whoever.

If I was discussing something with a colleague and, particularly supervisor, like let’s say favorite dishes and said “I like soups” and yiu asked “what’s your ex husband’s favorite dish?” it would make no sense to be. So asking about his ex wife doesn’t make any sense

Lack of boundaries has been a problem for you in every employment. So just focus on boundaries. Don’t argue with supervisor, move on