I'm pretty sure triggers are a lot more serious than that. They're things that remind people of psychologically traumatic things that happened and whatever. So someone who was sexually assaulted would have triggers in the form of rape jokes and things like that. Or at least, that'smy understanding of it.
Then Kankri was just being a dick by overly reminding people of hw much he's considering them.
While that's a fair assumption, especially as that's how it's used in real life, it seems that Kankri's use of the word is a lot more informal - he seems to use it in the meaning of 'something that will make you angry'. ('TW: oppression, culling, grub violence, lusis abuse, hemophobia, pails, slurries,' to cull from his hash text.) Plus his blithe acceptance of Porrim's 'being triggered' by his 'appropriation talk'. He also mentions the term 'Rustblood' being highly triggering. (Presumably to himself, since he 'highly implores' Karkat not to use the term.)
The way I read it, he wants to keep everything strictly academic in his conversations, and thus wants to steer around any topics that might make anybody irrational, emotional, or defensive and hinder frank discussion. Ironically, this basically ensures that his discussions on how to fix peoples' problems never actually addresses the problems of the people he talks to.