Most people give to charity because it makes them feel good - knowing you're helping people is a warm fuzzy feeling that most people enjoy. Obviously this can lead to irrationality pretty easily - look at the ineffective charities kept alive by nice narratives - but if we take that as the base reason, then standard human loss aversion can explain splitting. Your goal isn't to improve the world per se, but instead to have your money improve the world. In other words, the argument about linearity of utility disappears, because one bad decision will destroy all the value you get from charity, and since that value is partially independent of the expected value of the good done in the world, this can happen even if you're investing in the charity with the highest EV.

I don't 100% agree with this, but it's fairly close to my gut feeling - I split my political donations, but not my humanitarian donations.