Well, sometimes family wants to know our source of income and make sure it is a clean source of income. Many people know that there are a lot of scams on the internet these days, and our family doesn't want us to be those people. Therefore, it is very important to let them know about the basics of what we do on the internet, so that they know too. However, as you said, it all depends on how your family perceives you. However, I feel that it is important.
You're right, our family sometimes wants to know our sources of income to ensure that we're earning good money and not stealing from others, however, our parents understand the pain it is to steal from someone to meet our daily needs because they wouldn't be happy if someone scammed them out of the money they need to support their family, so they want to ensure that we're not earning from the wrong source.
However, I have faced a similar situation in the past. My parents didn't ask me how I was making money without troubling them, but when one of my uncles noticed that I had changed and stopped asking for help, he informed my parents that I was engaging in fraud and scamming people to make money, which is why I no longer bothered them, my parents asked me how I was making money, but I didn't tell them how much I was making, I didn't think it was wrong of them to find out, all they wanted was to make sure I wasn't taking advantage of people to get money.