At what point does OP's right to free speech in a public forum trump her right not to be offended

The line is not simple offense. It never has been. This is one of the common misconceptions about harassment.

An action becomes harassing(again, in the general case) when the intent is to annoy or harm. That often means that the action has to be directed at the victim, the subject knows or reasonably should know that the action is annoying or harmful, and he intends for that to be the result. There often has to be a pattern, as well, although that's not true everywhere.

Let's show a more concrete example here. Let's say I am having a discussion on /r/AskReddit about the environment, and I advance some horrible notion, like "All cats should be euthanized". Even if someone takes offense, that's not harassment. There's no intent, as it's not a directed statement, and it's part of a reasonable discussion on the topic. There's also no pattern.

Let's say I take that same statement to that same discussion in /r/catlovers. We're closer now, because the potential for annoyance/harm offense is higher. But still, if it's a reasonable part of a discussion, then intent isn't there.

Now, what if you go into /r/catlovers and randomly post that all cats should be euthanized. Now we're most of the way there. Your post would be very likely to annoy/harm, and it's reasonable to expect that you would know that. You also have no particular purpose to post that, so intent becomes much easier. If you continue posting repeatedly, you'll also establish that pattern we talked about.

Of course, this is just an off-the-cuff example. All of these situations are fact, context and locale-specific.