If you do not want to use gapps on your device, but still need some proprietary apps frequently updated, there is a solution. You can set up a script that will fetch apps that you need and store them in a F-Droid repository.

I’ve set up a repository with some stuff here, but only for testing purpose.

Steps to reproduce (and sample commands):

• Install fdroid server package. (fdroidserver Debian package):

	sudo aptitude install fdroidserver

• Create user for repository and log into it:

	adduser repo
	su repo

• Create fdroid simple binary repository:

	cd ~
	mkdir -p repo/repo
	cd repo
	cp /usr/share/doc/fdroidserver/examples/config.py repo
	#edit config.py

• Get python googleplay-api:

	cd ~
	git clone https://github.com/egirault/googleplay-api

• Take a device with gapps (emulator is OK) and get GOOGLEPLAY_ID. Remember, you need GOOGLEPLAY_ID, not ANDROID_ID. Then add it (and your login && password or token) to ~/googleplay-api/config.py. Set up the rest variables according to what you desire.
• Get my files:

	wget -O ~/googleplay-api/version.py https://der.ttyh.org/files/version.py
	wget -O- https://der.ttyh.org/files/proxy.tar.gz | tar xvf -

• Use get.sh for adding packages. For example, ~/get.sh org.mozilla.firefox. Then run cd repo && fdroid uptade -c
  • If you want, you can fill in ~/repo/metadata/org.mozilla.firefox with package information
• ~/do.sh will update all the packages, add it to cron, if you want
• ~/repo/repo is your repository. I made a symlink from /var/www:

	/var/www/repo -> ../../../home/repo/repo/repo 

• Add it to F-droid.