Your parents are not bad parents. Bad parents are women who kick out their sons to live on the street at 15 years old because he told her to make a choice between her abusive partner and him, she chose the abusive partner (seriously, this happened, not to me but to a friend.)
It seems to me like you haven't grown up yet, or at least haven't grown a spine capable of standing up against your parents yet. It's not the easiest thing to do granted, but there comes a time when every guy pretty much has to tell his parents "Look, I'm an adult now, stop treating me like a child or fuck off".
Saying that however, they haven't seem to have done anything to warrant such an outburst. Not everyone likes anime. I don't. I've tried to watch it, just can't enjoy it. It's not about what's on the pillow, it's the fact that as an adult you are using a pillow case witch a picture of a fictional character on it. You could make a pillow case with Kharn the Betrayer bathed in blood yelling "BURN, MAIM, KILL!" and it still wouldn't make a difference, that sort of stuff is supposed to stop around 14.
Secondly, your mum made some jokes. I refuse to watch reality tv, my mum loves it, she winds me up about it. I then wind her up back, usually along the lines of "It's a sad day when the only thing you consider worthwhile involves pretty colours and a phone in vote!" It's all in jest, we don't think any less of each other for it.
Ultimately, everyone thinks they are correct in their own minds. You see nothing wrong with the pillow and you take offense at people making jokes. Whether that means you have maturity issues or not, you're not going to change because some people on the internet tell you to. Infact you're probably looking for validation more than anything, which probably means you do sense there might be something wrong with you, because you felt the need to ask the question to see how many rallied around you and tell you that you are correct.
Life for the most part is having to stand up on your own though. Like everything else, this is something only you can put right, whichever way is best for you.