"Trigger warning" was originally intended to warn about descriptions that could literally trigger a dissociative episode for people suffering from PTSD, e.g. victims of child abuse or sexual violence.
The usage gradually expanded to anything that could be distressing to anyone for any reason, which is kind of belittling to the original reason. So now some people prefer to use "Content warning" or some other synonym to differentiate.
It's nothing to do with the word "trigger" being associated with guns.
Stanford seems to have beaten the "anti-woke trolls" at their own game.
> The phrase can cause stress about what's to follow. Additionally, one can never know what may or may not trigger a particular person.
It carries almost zero information. Who is going to read "trigger warning" and think "oo they know that I'm highly sensitive about this specific unknown subject. I don't want to get triggered, I'll stop!"
Contrast it with something like "spoilers" where everyone agrees on what it means and people generally really don't want to read spoilers.
To the extent it was, it was based on a completely misinformed idea of how triggering in PTSD works. In practice, if not in intent, it has been, from the beginning, an appropriation of the language of PTSD to serve as a vehicle for expressing personal value judgements and content preferences that have nothing to do with that. And there is research, IIRC, that it is actually counterproductive, inducing stress without helping anyone avoid PTSD triggering.
The phenomenon you are referring to - appropriating the language of PTSD for concerns of politics, taste or personal offence - is exactly why some people advocate replacing "trigger warning" with "content warning" or similar (and not because of associations with gun violence, as OP asserted).