I would say that browser usage, demography (country distribution etc.) and navigation paths (bounce rate, funnels, etc.) within the site are all important data points to optimize a non-profit website. I'm not sure anybody can make a point for GA to be life changing for that site, but the opposite is also true (the saving in privacy from visitors is not going to have a game-changing effect).

I also think that a pragmatic organization should focus on a few very important battles that it thinks it can win, rather than trying to fight everything in the name of ideology.