On its face, if you're dealing with "my truth" as opposed to a concept of objective truths, one might expect the vindictiveness and the accusations to come from the side of objective truth. If you think that truth is objective and you believe that your perspective is in line with that objective truth, it's easy to see how you could be a dick about it.
The thing is, if you mingle with enough people, you notice trends. I've been in several interactions with religious people, usually older, who regard homosexuality as a sin and draw the line on attending a gay wedding, even if it's the spawn of a personal friend; but, they'll still welcome gay people into their homes and treat them like anybody else. Even in my lifetime, there have been well documented friendships across the political aisle. For all of Sam Harris and Maajid Nawaz's faults and disagreements, they can beat the hell out of each other's ideas for hours and still be friends. Can anybody really say that they don't think that Bill Maher and Anne Coulter have hooked up at some point?
These are all people who believe that truth is a matter of objective reality. Sam Harris made much of his career by pushing the concept of moral truth without religion.
So, why is it that there seems to be a clear connection between the "my truth" people and people who engage in bigoteering and refuse to even associate with opposing opinions?
Well, if we believe that truth is objective, and it doesn't and can't simply live between your own ears, conversations about hard ideas are still regarded as attacks on your ideas and your blind spots rather than attacks on you directly. If it's your truth and somebody thinks that you're wrong, it's an attack on you as a person whether your detractor intended it that way or not.
If there's a mutual understanding that the truth is something that we're trying to discover together and that we're fighting about what it is and how to get there, verbal altercations can be had in the moment followed by beers later. If we're coming at anything from our personal truths, there's nothing to debate. There's only mud to be slung and feelings to be hurt.
Now, maybe the mud slinging and the feelings are more right than the pursuit of objective truth through debate; but, that assertion would still require an argument. Namely, "my truth" is a self-refuting concept in most ways.
Even if it weren't, imagine a person who gives credibility to "my truth" on a jury. Paint your own picture.