1. People have a right to be offended
This is the most important point so I'm putting it first. Just because you, personally, don't find something offensive doesn't mean that somebody else won't, especially in cases of racism, sexism, transphobia, etc. And that other person will be perfectly justified in taking offence. It's not being 'oversensitive' or 'harshing your squee' (though if it does make you feel guilty you might want to take another look at the source material). In pretty much every case, it's a legitimate response to something hurtful, and should at least be treated with respect.
(as a sidenote: not being offended doesn't make you a bigot. Belittling people who are offended kind of makes you a dick, though)
2. Our fandom is important to us
We all love fandom. It's an escape from the 'real world', a chance to be creative and meet people from all over the world (at least that's what Hetalia has been to me). So how hurtful must it be when your release valve turns around and bites you in the arse, figuratively speaking? When characters you love and have invested time in become mouthpieces for cheap, offensive gags that you've heard too many times already? It really, really sucks. Yeah, it's not the end of the world, but it's your stuff, dammit, and it hurt you.
Everyone has their own way of dealing with this bit. Some people defend their fandom to the very death. Some people just ignore the problematic aspects. Some people don't. That's where we come back to point 1, and being offended.
3. Resources, resources!
For those of us who weren't aware of our privilege before we got on the internet, the web has a brilliant range of stuff for us to read. Maybe this way, we can be better informed next time something like this rolls around. These links on scans_daily's profile are a great place to start.