When using stock find-file or counsel-find-file, is there a way to ignore certain files that I almost never want to open by hand? Examples include .elc files and backups.
Yes, use counsel-find-file-ignore-regexp.
For the simple example you provide use
(setq counsel-find-file-ignore-regexp "\\.elc\\'")
The are more examples in the docstring for that variable.
completion-ignored-extensionsdoesn't work in that context? That's what ordinaryfile-name-completionrespects. See (elisp)File Name Completion and (emacs)Completion Options. Of course, that's just extensions... – Drew Jan 10 '17 at 5:58counsel-find-file-ignore-regexp, one of the options is to usecompletion-ignored-extensions. – John Wiegley Dec 13 '17 at 0:12