then does it not also stand that someone's words can have a negative impact without a necessarily negative intent? To speak is to act.

The important factor of words is that they drive action. A person speaking without hostile intent behind their words is both unlikely to act on them, and unlikely to repeat those words to the extent to create a culture or situation that encourages action. My point is that I can see why terms like "die cis scum" could be non-hostile and perfectly fine to say, but regardless of how much hatred people feel from it, if it is a message created from dislike, it is just as bad as any other.

I think you would be surprised at exactly how much the sort of people who cheat would be also driven to hold the ideal that nobody else should cheat. Most people who cheat do so out of momentary lust or dislike of a current relationship, etc. Not out of dislike of monogamy. Regardless of this, by cheating, they open up the vector of "well they did it!" which slowly erodes away social laws. If enough people start cheating, it will become normal and regular to do.

My coworker got hit by a car a few years ago. The lady driving sure as hell didn't intent to hit her with a car.

Hitting someone with a car is not akin to saying something online. And I am sure I wouldn't go around calling the person who hit your co-worker a murder or a monster because of the action, unless it was intentional.

The only way that words that do not carry hatred behind them can be seen as such is through misinterpretation, or through certain "jokes" becoming so common that it becomes an undercurrent of how you act. And, honestly, the latter only tends to happen when there is some undercurrent of dislike or hatred. As to the former, I am not a fan of saying "you are responsible for how others interpret what you say", outside of when a person mistypes or misspeaks.

If you call a person a derogatory name as a joke

I am not defending that sort of situation. The line is drawn when the literal words you say have a meaning that is directly harmful. You can't go to people saying "I fucking hate all of you" and later say you meant to say "love", and you are responsible for all the setbacks from that action.

I am defending a situation where a person says something that is entirely and totally harmless in context, but is interpreted as hateful by those outside of that context. See: "die cis scum".

Of course, my other point is that if you are typing "die cis scum" and you actually are doing so out of dislike or disdain for another group, than you are in the wrong.