I agree that it should be "affect". Affect doesn't look wrong to me:

  and technology choices made in Firefox can and do affect Thunderbird, just like they effect e.g. Zen Browser or Tor Browser.

I'm no expert on the rules of english, but I think maybe it would be slightly more gramatically correct to say that "choices made in Firefox can and do have an effect on Thunderbird". I would probably have phrased it like that. Maybe that's why it looks wrong to you?

English is a bit of a bastard language IIUC, and so we accept the way you've phrased it too, but in that case it should be "affect".

I hope this helps rather than making things more confusing! ;)