I think intent matters. I think the reasons why we do something are relevant in assessing how we should be judged on what we do. I think some of the factors that are important in determining intent (and these do not limit any other factors that may arise in a particular context) are—
(a) what the person thought they were doing:
(b) what they were trying to achieve:
(c) whether they were acting in good faith:
(d) what they actually knew about the situation they were in:
(e) what they could be reasonably expected to have known about the situation they were in.
I think intent matters because I dislike the idea that someone is just as culpable for being accidentally offensive as they would have been if the offense had been malicious and intentional. That doesn't sit comfortably with how I think about morality: surely hurting people on purpose is worthy of more blame than doing so accidentally?
Most of the discussions I have seen about intent have been in the context of someone being offensive and then saying that they didn't mean to be, as a kind of excuse for the harm they have caused. For better or for worse, it usually comes along with an apology. On the side of whoever has been harmed, someone (quite rightly) points out that the fact that the harm wasn't purposefully caused doesn't mean that it didn't happen or wasn't real.
Where I break with both sides is that I just don't find a lot of the claims of complete innocence very credible.
An example of something that I do think was done innocently—and it's kind of a ridiculous example, but I think I can use it to make the particular points I want, so I'm going to run with it:
A few weeks ago I went to the birthday party of a good friend. There I met a friend of hers, who was a very good costumer. We got to talking about corsets (as you do), and she said to me that corsets were better than bras for large breasts, because they give better support and take less pressure off the spine.
I wasn't offended by this, but it did sting a little and it is one of the things I carried away from the evening. It fits in with a whole lot of stuff I have going on about body image and the curse of shopping and what expectations my professional career will place on how I look and dress.
The first point I want to make with that example is that I can't infer any sort of purposeful or reckless attempt to upset me or poke at wounds from that conversation.
The second is one about words having meanings and meanings being contextual: if I had been in the midst of a conversation with that same person about body image and the curse of shopping and what expectations my professional career will place on how I look and dress, and she had said the same thing, I would have been much more upset and I would not have found a claim that she meant to do no harm particularly convicing. This is because I work in a fairly conservative office and suggesting that I wear corsets would clearly not be a reasonable response to me talking about how difficult I find buying work clothes.
I think it is fair to expect that people who are debating things in good faith will pay attention to the conversation they are having, and take contextual clues from that conversation (rather than from how they talk to other people in their lives). I think it is reasonable to expect that people will turn their minds, even if only briefly, to thinking about what the likely sore spots are for whoever they're talking to and then (if they are determined to continue the discussion in good faith) not say things that are likely to poke those sore spots.
There is, of course, a limit to what a person can be reasonably expected to know about a particular thing (either a topic, or what the sore spots are of the person they're talking to).
But, for example, I think it can be taken as read that someone who identifies as leftish and who is bothering to engage in explicitly feminist discussion should be aware of basic dialogue about how women are (often) treated in discussions (hysterical! irrational! devoid of reason and unable to make coherent points! simply ignored!); and therefore if that person should choose to use argumentation techniques which rely on ad hominim attacks like "calm down, you're being irrational" they have absolutely no basis on which to claim that they are totally innocent and had no idea that their words could give offence when, inevitably, someone is offended.
This is what I mean when I say that I think intent is important, but that claims of a lack of intent should be critically examined.
I think part of my problem with the discussions about intent that I've read is that they almost invariably take place in a context where (at least initially) everybody is acting in good faith and nobody is trying to be malicious and hurtful. In that context it isn't so much that intent isn't important as that if everybody is claiming that they genuinely had no idea they were giving offence and there's no reason to doubt that, the conversation must of necessity move to what the person should have known.
And maybe "you ought to have known X and Y and Z; these concepts should have been familiar to you as a regular commenter on this forum/a member of Group B/a resident of this country/a citizen of the world" is a tougher sell than "your motivations are irrelevant", I don't know. Whatever else it is, communication is complicated.