Privacy Badger dev here.
I think the biggest concern is to only install extensions from developers and organizations you trust.
As for your browser fingerprint, on the one hand, the more custom your browser setup, the more you stand out. On the other hand, Privacy Badger exists to reduce pervasive, non-consensual tracking. We especially aim to block pervasive fingerprinters, along with other obnoxious types of trackers.
More about Privacy Badger below, adapted from https://privacybadger.org/#Is-Privacy-Badger-compatible-with...
While there is a lot of overlap between the various manually-edited advertising/tracker lists and Privacy Badger, unlike list-based tools, Privacy Badger automatically learns to block trackers based on their behavior. This means that Privacy Badger may learn to block trackers your list-based tool doesn’t know about.
Besides automatic learning, Privacy Badger comes with other advantages like cookie blocking, click-to-activate placeholders for potentially useful tracker widgets (video players, comments widgets, etc.), and outgoing link click tracking removal on Facebook and Google (recently updated, see https://www.eff.org/badger-link-tracking-protection-update).
Privacy Badger is also a political tool. Privacy Badger sends the Global Privacy Control signal to opt you out of data sharing and selling, and the Do Not Track signal to tell companies not to track you. If trackers ignore your wishes, Privacy Badger will learn to block them. By using Privacy Badger, you support the Electronic Frontier Foundation and help fight for a better Web for everybody.