I did read the source, and they're using a Google AI classifier product, "perspective AI", and even in the description of the product, it raised questions about its suitability.
At this point, most people in the space are pretty comfortable with the idea that AI models don't eliminate bias, in fact it can amplify it.
I'm not saying "there is no way to attempt to measure toxicity", just that based on the specific design of this study, if the measure of toxicity was biased against ANY political discussion, that would be an alternative explanation to the results.
You should read the article, if not the study itself. Its design smells suspiciously like that of an honours thesis as opposed to a grad project. Not just because of the AI... Mostly by the way they defined what constitutes participating in political discussion.