Would this specific one affect Tor's anonymity and privacy?
There's no real way of knowing in advance, without looking at the source code. If the source code isn't available - i.e. if it isn't an open-source project - then there's no way to check.
[Note that this does appear to be in an open format, but I can't immediately see where the code is kept. You'd either a) have to trust Mozilla, or b) find the code and go through it.]
The problem is twofold:
- The add-on could be creating its own connections to the outside world, bypassing Tor completely. If it can do this, then it can expose your real IP address.
- By installing add-ons and extensions, you change your browser's fingerprint, making you stand out from the rest of the crowd of Tor users. (See other posts marked with the fingerprint tag to get a better understanding of this.)