I'm not a very organized/clean person, so just keep that in mind when I give my opinion.
If it was my first time away from nagging parents and chores, I would hate moving in with someone who stuck me with "you gotta do this and that this week on top of cleaning up after yourself." I'm fine with cleaning up after myself, makes sense. But I can go a few months before thinking its time to pull out the vaccum.
And if you have the shedding cat, I'd assume you'd be the one cleaning up it's hair mess. If I didn't have a pet but was asked to vaccum up the hair from the carpet weekly, I wouldn't. Plain and simple.
If you have the animal and the high standards of cleanliness, you're gonna be the one doing the cleaning. If you don't like it, move in with other clean freaks.
Just my opinion on the matter. But hey, maybe your roommates are cleaner than me.