It's a bit difficult to explain, but I'll try.
In the current political climate, the left and the right have been divided by the public consciousness into the following dichotomy:
The left is overly sensitive and looks for things to be offended by.
The right is concerned with maturity and personal responsibility and anti-political correctness, where those things are defined primarily in contrast to the left's perceived over-sensitivity.
Simultaneously, there have been a lot of trends in various communities (software and otherwise) to formalize rules of conduct and push out people who are more naturally aggressive in tone.
Through that lens, this behavior has been seen as "left-leaning." So in contrast, the right-leaning behavior would be letting everyone behave as they want with the "free market of ideas" being the primary driving force for change rather than any set of enforced community standard. (You can see the parallel with the typically "conservative" economic perspective.)
I hope you can see the general trend.
So what the grandparent is saying is that it's not REALLY about left vs. right, without explicitly contradicting the beliefs of the common social consciousness.
Edit: The comment above that says, "Different people have very different beliefs what is to be considered 'heated', 'hateful' and 'treating well' or not" would be considered "right-leaning" through the common lens because it's implicitly positing that there shouldn't be a common set of community standards (with the implicit supposition that you CAN'T set a common set of community standards because there will always be people who disagree). Not picking on anyone, just using an available example.