You should check out the alternative app store F-Droid. It is completely free software apps, and all are Ad-free and high quality. There are alternatives or replacements for just about anything you might want, and you don't need Google anything.

I've been waiting for some way to synchronize contacts on FM for years. According to posts on the support forum, they are pretty close to having CardDAV support implemented. Fingers crossed that they roll it out soon.