You are allowed to create problematic characters, and you should, but at the same time, there should be some acknowledgement that they are problematic.
For my story, one of the main issues was the fact that the character was supposed to be a fundamentally good person, and he cannot be both a good person and a person who ignores the need for consent. I didn’t realize when writing him how problematic a character I had written him to be, because I hadn’t intended him to be that problematic, and so there was no real acknowledgement that he shouldn’t be doing what he was doing. And, at least to me, that reads like an (implicit) agreement with what he was doing, which is bad.
In regards to the second part of your question, I think there are basically two parts. First is whether or not the writing is “pc”. In my opinion, writing should be, if not advocating for being good, then at least not romanticizing being not-good. And part of that means making sure that your writing isn’t perpetuating harmful things like racism, sexism, and rape culture. I’m not seeking to please everyone, because that everyone includes people who believe in harmful things. But, at the very least, I am trying to please myself, and that means writing in a way that won’t harm others.
I was going to say that I won’t tell other people what to write, but that’s not quite true. I believe fairly strongly that people shouldn’t write stories that will harm others, and if that makes the stories PC, so be it. There are ways to produce and generate discourse regarding civil and societal issues without hurting vulnerable groups of people, and so, in my opinion, that’s how you should write.
The second part is whether or not what I write will trigger people. And, honestly, some of it probably will, because most things will trigger at least one person, and I write about dark enough things that they will probably trigger many people. That doesn’t mean I’m going to stop writing about those things. What I will do is make sure I write those things in such a way that they don’t romanticize those negative things. I will do my best to not romanticize rape or abuse or slavery or suicide or self-harm or mental illness or other things like that. And sometimes I’ll fail, and that’s why I need people to tell me the problems they see with what I’m writing.
I hope that answers your question.
This is a good question and a good answer.
Are you going to trigger a reader? Yes, it is possible, but that isn’t an issue if you address the other half of this question, which is, what if your triggering character is a dick?*
If your protagonist is a dick, who walks like a dick and quacks like a dick and benefits from that behavior and is never shown to grow beyond it or suffer for it, then he has no business being a protagonist.
To paraphrase elumish, who already put it so succinctly and elegantly, readers will not penalize you for triggering them, but they will call you out if you write from the point of view that this dick is not a dick.
*problematic for reasons that used to be lumped under ‘not pc’, but now are clearly defined under their proper terms: racism, misogyny, homophobia, etc.