This is due to churn on the compiled files right? The fix would be to compile these files someplace outside of dropbox. (Because the important artifact you want to back up is source code, not binaries). Depends on your language / build tool for how complicated this would be...

CMake encourages out of tree builds. I find them superior to in tree builds in most cases. But if it is just a random utility that I'm compiling from the Internet and do not intend to dev on, in tree works fine for me.

A suggestion off the top of my head would be writing a script that pauses Dropbox syncing before running a compiler. (From a quick Google search, there seem to be a couple of scripts already written that do this.)