...how is this NOT yuri?

The anime tells the 1st of 3 story lines in the Fate/Stay Night game, so I'm not sure if the fact that Rin and Sakura are related is included. The 3rd story, Heavens Feel, includes Sakura's relevant background information.

You can find spoiler synopsis for the 2nd and 3rd stories here:
http://www2.ocn.ne.jp/~typemoon/fate/index.htm

Kayako said:
How is this 'incest' or 'sisters'? Rin and Sakura aren't related last time I checked. Please correct me if I'm wrong, I never finished watching the series, but I'm removing those tags for now.

So you never watched the series completely and never touched the game apparently. What sources are you basing those claims on? In short, where did you check?

Don't change the tags if you don't know about the series. At least ask first at someone who knows.

I've never played the game(I want to, though). But in the anime it's heavily implied(I can't recall if it's explicitly stated or not) that the two are sisters. And yes, they are, regardless.