There is no feature that ignores and then subsequently removes or hides one user's topics or replies from another. We had something like this on the old system, but it isn't a part of the built in feature set on the new system, nor is it offered as an addon or plugin by the developer or a 3rd party.
We're trying to identify the feasibility of such a feature with the new system, and have a few ideas that we'll be testing in the future. Ignoring someone sounds like a simple thing to implement, but it's not clean. It can create confusion in a topic/thread, especially in question and answer scenarios, resulting in potentially duplicate answers, quoting of persons ignored by one but not by another. So it can get messy.
Stay tuned for further updates.