No, some having MORE buttons than others, and in unusual places, is perceived as being sensitive. If someone is sensitive to, say, politically incorrect humor...okay, that's fine. Taken alone, it's not enough on its own to deem someone overly sensitive. People have different buttons, like you said. I, for instance, am sensitive (if that's what you can call it) to crude gender humor in the sense that it offends my sensibilities when I hear it, and I have an emotional (albeit slight) reaction to it by becoming irritated.
But when the number of things that a person is sensitive about exceeds a certain point (for instance when the person becomes the "see no evil, hear no evil" type), then I think it is fair to call that person sensitive. I have met quite a few people whose number of buttons were ridiculously high, to the point that I could not discuss or have fun about anything with them. That is what (I at least) consider to be overly sensitive.
My apologies on this. allow me to clarify myself, because I have DEFINITELY experienced this as well. Some people are extreme, or so sensitive that they should not be hanging out with the groups they subscribe themselvse to... and it's even more frustrating to know that they refuse to budge to accomodate themselves, they expect the world to change for them.
What I was more referencing is exactly what Trinity said better: Sensitivity at all is seen as feminine, which is seen as weak. BlackCat claimed himself not at all sensitive enough to be considered that, but my rebuttle is he was, and shouldn't be quick to refute that. I added that statement in to show it's not necessarily a bad thing, because what one person thinks is sensitive another does not, but that the stigma for sensitivity is definitely prevelent in his own words.. making him quick to reject the idea of being sensitive.

I actually have pretty high Fe, and I will not strive to offend, but there are some people that it's impossible NOT to offend.
I'm weird sometimes, too--I'll get in a mood where someone's phrasing can irritate me, and I get offended that they didn't try to be more careful of how they came across, because I know I would have in the same situation.
I like to think of myself as having thick skin, but if you're close to me, it's a lot easier for you to hurt my feelings. If you're just an acquaintance, I'll probably let it roll. If I care about your opinion of me, you can hurt me.
^ I relate to this a lot. The more I open up to people, the more open I become to their insults hurting.. a fair system for the most part, imo.
I'm a huge believer in intent as well.. picking on BlackCat again.. there have been a couple of times that he's said something to offend me.. BUT. Recognizing that his intents probably were not meant to hurt, allowed me to just take a step back, calm down, and then go to him to explain that that was hurtful, and although I don't want him to think he has to shut up everytime I sign on.. I would appreciate refraining from that sort of comment in the future around me at least.
Had it been that I felt he was attacking me "safely" via joke or sarcasm, my offense-o-meter might go way off, which I would react to by (most likely) telling him his faults, and then proceeding to never talk to him again so that he does not have the opportunity to offend in the future.
Had a total stranger said the same thing, I probably would not have even noticed, and it at best would have made for interesting conversation later on with friends.