My sister and I both live at home, and at the moment, both my parents are on a 4 month holiday so it's just us two. My sister got a cat last year (even though I'm very allergic to it and fleas) which has been alright cause it's mostly an outdoor cat. But last week, my sister decided on short notice to move in with her boyfriend and can't take the cat with her. She wants me to look after it even though I'm really allergic and generally don't like it anyway. What should I do?
I don’t think you should take it. It was shitty for her to get it in the first place while living with you, and it’s utterly unreasonable of her to decide to foist it off on you because her life decisions are making her unable to care for it. This cat’s welfare is not your obligation, and it’s not fair to you to put you in this position.
Also, it’s worth noting that you’re likely not going to take great care of an animal you don’t want, don’t like, and have health issues related to. Even if you intend to and try really hard, resentment builds up and can affect the cat’s quality of life. That’s not fair to the cat.
Help her rehome the cat if you’re worried about it’s future care - or if you’re worried she’ll just abandon it - but you definitely don’t have to take it yourself.