I wish I could tell my best friend to shut up about her eating disorder
Why do you want your best friend to shut up about her problems?
It's nothing personal I don't agree with eating disorders
Being a good listener fosters meaningful relationships with those around you. You should help your fiend get the support they need rather than shutting them out.
I DON'T SEE THE PROBLEM.
Clearly your friend's eating disorder means nothing to you, but this is still your best friend that you are talking about, and it is obviously a problem to her.  Instead of just shutting her out, or telling her to shut up, you should direct her to someone who can help.  Not only will this benefit your friend, but it will save you from having to deal with a problem that doesn't seem to concern you.