This post has a number of misconceptions that I would like to correct.

It is a truism within the Effective Altruism movement that you should not diversify charity donations.

Not really. Timeless decision theory considerations suggest that you actually should be splitting your donations, because globally we should be splitting our options. I think many other effective altruists take this stance as well. (See below for explanation.)

Nonlinear Utility Function:

If your utility function is nonlinear, this is fine as long as it's differentiable.

Not necessarily. You are leaving out an important point here, which is that this argument only goes through when differentiability implies that on the margin your utility can be well-approximated by a linear function. That only works if the charity's budget is large relative to your contribution. If you're donating large amounts of money (say over $10k to a small org like MIRI or CEA), this may not hold and it's not necessarily irrational to donate to multiple organizations.

Risk-Aversion:

Also seconding what Squark pointed out, which is that risk-aversion is a feature of your utility function, not something that you tack onto your utility function. Wikipedia has a good description/picture, but basically, it's rational to be risk averse for gains in widgets if and only if your utility function has diminishing returns to widgets. (It's also worth pointing out, since by your phrasing I'm not sure whether you know this, that literally everyone's utility function is nonlinear in literally everything.)

Since this is the case when "widgets" are donations to a particular charity, the socially optimal global allocation of funds does not have all the funds going to the single highest-EV charity. If you follow timeless decision theory, this suggests that you should make the split that you think would be optimal if everyone else who followed TDT made that split (which accounts for a sizeable amount of donation).