Would the term "brown people" be offensive to you?

Yes.

I'm not sure I would say offensive, but I certainly wouldn't use it and would question someone who did

WEll, I was going to say no, because I know a lot of people who refer to themselves as brown/brown people. Maybe that's one of those things you're allowed to call yourself but other people can't use if they aren't part of that group?

yes, No "people" should be called by their skin color. White people, brown, yellow, red. whatever.

I've heard it used a lot, by white people, brown people, and by TV commentators. It seems very normal to me as an alternative to "people of color," I guess. It includes many minorities.

However, since everyone here seems to think it's offensive, I will watch more closely where and under what circumstances I hear it in the future, and reconsider.

I'm usually pro-sensitivity, so I'm surprised I'm one of the only people here who doesn't think it's offensive. 
And now I can totally hear the voice of this guy I used to work with, saying it.

Interesting. I've never thought to call anyone "brown people" but we say white people and black people...

Nope. I'm Indian and I call myself brown
So does my white husband! Lol

As it is said in the above comment, it wouldn't matter what color she said, she did intend to offend. But that's just Ann Coulter, she lives to get herself in the spotlight for being "controversial" when really she is just being an asshat. 

...She calls black people "brown" bc their skin is in fact brown...

So do I.  Having grown weary of all the "PCness" we're bombarded with, it makes no sense to me at all to refer to anyone as black.  I've never, ever seen a truly black person... I've seen many brown people.  So, if I refer to an African American by color, I use the term brown.  I don't see how anyone can find that offensive.

I'm not "white" technically. It doesn't offend me to be white. I call black people black, no one has ever been offended by that. I would call an Indian person Indian or Asian and Asian first though before I called them brown or some other color.

Two of my grandsons were fathered by a Mexican man and they refer to themselves as brown. I see nothing wrong with it as long as it's not used in a derogatory way. They are the cutest brown boys you've ever seen too 

It's funny you ask that because the other day, 2 women and I were having a conversation and they both happened to be black. One of the women and I had witnessed something between a man and another teenager and she was telling the other woman about it. As she was explaining the situation she went on to describe the guy we were referring to and she called him by name and said, "You know him. He's a really big black guy.".

I adore both of these ladies but my spidey senses went up because I was surprised to hear those words. I know that I wouldn't have described him that way because I thought people found it offensive. Although, I did wonder how they would have reacted if I would have described the man as "a really big black guy". I guess I just always thought people would be offended by that. Maybe not? 

My ds did this, too.

When my ds was much younger (maybe 3 or 4 years old), he absolutely horrified me one day by telling me (loudly, in public) that he didn't like "black" people. Of course, I immediately started explaining to him that some words are hurtful and shouldn't be used, etc. He kept giving me the strangest, most confused look, like he couldn't figure out what the heck I was talking about. I worried that he wasn't understanding what I was trying to explain to him, so I finally referred to Michael Jordan, who was my son's hero at that point in his life. I started to ask him how he would feel if he had said words that hurt Michael Jordan's feelings, blah, blah, blah...until finally ds interrupted me and said "But mom, Michael Jordan isn't a black person. He's brown!"

It turns out that my ds's definitions of who was a "black" person and who was a "brown" person were not at all what I'd expected. According to him, "black" people are people who have spent so much time artifically tanning that their skin has turned a nasty, unnatural, leathery color.  So.....when he said that he didn't like "black" people, all he meant was that he wasn't a fan of the whole horrifyingly-overly-tan-burnt-to-a-crisp-look, which I'm not all that fond of either.