It would depend on what is meant by being triggered.
To a large extent we can choose whether to be offended by something. We can decide how we respond to a form of words we might not have chosen, and it often seems like a lot of "offense" is manufactured. The terms we're supposed to use apparently change with the tides, and some people set themselves up as arbiters of what is offensive and what is up to date. I remember a case somewhat recently in which a senator - I think Senator Hirono from Hawaii, but could be wrong on that - commented about the term "sexual preferences" being outdated and offensive because the correct term was "sexual orientation", although the person who had used "sexual preferences" was a lesbian and figured she could decide for herself what term to use to describe the fact she had a preference for other women.
But then there's another aspect because sometimes being triggered is a physiological matter, or a deeply rooted psychological/psychiatric matter than we can't necessarily consciously override in the moment. If someone threw a bucket of blood, vomit and feces over you the chances are you'd be triggered in some way - primarily in the form of revulsion - whether you decided to be triggered or not. Likewise people who have suffered extreme traumas may exhibit an amygdala-based response that makes no sense to someone who doesn't regard the specific prompt as representing any threat, let alone a substantial threat.
So I think the short version is that, as is often the case, a meme sums up something that is kinda-sorta-broadly true but misses much nuance.
