It's also important to understand that furries are an incredibly diverse bunch, with millions of little cliques that all have their own definitions to what it means to be a furry, and what they enjoy doing.
Some definitely worse than others.
I can't really say this with certainty because I don't know why you don't like furries and I don't know what flavor of furry your sister is. But if this is due to negative experiences with other furries, it's very likely your sister is not like that.
A common theme, sadly, with furries is that the most cringy and annoying ones tend to be the loudest, and that's why most people seem to have negative associations with the term "furry", but to a lot of us it's more of a hobby and social things, and we don't really bother people that aren't furries with the furry things we do, because, unless otherwise stated, they don't really want to hear about the weird shenanigans we're up to.
As for supporting your sister. Furries are often very open and supportive people, so she's probably gotten a nice group of friends in the community to do things with and likely won't need an awful lot of support from you.
I'd say the best thing you can do for her is to just to tell her you accept the fact that she's a furry and let it play no role in your perception of her, and just do the things you'd usually do as a brother to support and protect her, even if that sometimes involves things related to furries.
But do protect your personal boundaries. If you want to get involved, it's fine to ask her some things like what's her favorite artist and stuff, but if she starts showing or telling you things you really don't want to hear, or act in ways you find annoying, there's no harm in politely telling her something among the lines of: "Look sis, cool that you're happy and all, but I really don't need to see or hear that stuff, please leave me out of that."
If she's a cool sis, she'll just let it be without taking offense, because people have their own tastes in the end and stuff. c: