A rule of thumb that I use (which is by no means an official site policy) is whether I am adding to the topic, or just posting an 'I agree.'
Yeah, I think that's the most important thing to consider. In cases where relevance/newsworthiness is less clear, I'd make my decision based on whether or not I thought that my post would contribute something new and meaningful to the discussion. And, as I mentioned in the OP, I wouldn't add to topics likely to re-start old conflicts.
If I thought that making any post - whether as a reply or as a new thread - might cause conflict, I'd weigh (1) how important I thought the post was and (2) how many people I thought would be impacted by/interested in it, against (1) the likelihood that the topic would be upsetting to people [e.g. due to personal beliefs or past experiences], (2) the likelihood that the topic would be too controversial, and (3) the likelihood that arguments would dominate the thread.