Mine never really cared.
With the game they didn't mind that I played it, or that it was an online game. I annoyed them a few times for playing it a little too much when I was younger, but they were quite happy I was enjoying myself, and playing with some of my friends from school on it, which was good because at the time I always lived in small towns away from school, so never had much chance to play with friends after school in person.
As for the forums, they never really minded either. They knew I spent a fair amount of time on there.
They probably wouldn't have been pleased with some of the content that little 13 year old me saw, and discussed in, but I think they were happy that I was mature enough to be online.
And I sometimes discuss things that have been shared on here with them. Telling them things I may have learnt, or discussing their views on some controversial topics, etc...
I play the game much less now than I have done before, particularly these past 2-3 years, mainly as I've gotten older, had more responsibilities, and my friends have become less interested in the game.
But my parents still joke that if I'm on the computer I'm probably playing Blockland.