Well, you have 2 choices from what I've observed on this matter... Either make sure you unwatch the thread so you don't get any alerts (or just don't post in it and you won't automatically watch it), or ignore the member who started it and the thread itself will not show up at all.
But I agree it would be better with an option to ignore a thread just as easily as ignoring another member, because there will be times when a thread turns us away, but the original poster is someone we usually like to follow, so ignoring them would be counterproductive in this case.