Vampires aren't others, they're vampires. There is no rule that says you lose humanity from harming vampires. There is nothing immoral or inhuman about killing monsters.
The problem comes in with who gets it. In order to rock the True Faith, you need to have a high humanity rating. So you have to be reasonably sinless. Which probably sounds reasonable to people who are of a generally religious bent. But what that means is that the people who have True Faith are innocents, not people who go out and fight vampires by choice. Even choosing to go fight anything means your Humanity is too low to qualify for True Faith. But White Wolf authors were consistently incapable of wrapping their minds around that, and kept wanting to give True Faith (and the high humanity values it required) to “Witch Hunters” and other people who took the fight to the vampires. Which made for a somewhat interesting tactical encounter, but made no sense in world. To maintain a Humanity of 8 or more, you'd need to avoid accidental injury to others. Which obviously you couldn't maintain if you hunted fucking anything. Witches or otherwise.
I mean, if you look at official White World characters with absurdly high humanity and True Faith, then it's pretty obvious that you only lose humanity for crimes against mundane humans, and you can do anything you want to supernaturals, except diablerie.
Published adventures had a tendency to give the players a pack of 3rd-4th gen blood for various purposes, which allowed enterprising players to do a proxy embrace of a few fools and then immediately diablerize them, massively increasing your own generation. That annoyed some people and lead to a rule that vitae loses power as soon as it leaves the vampire, which of course created some plotholes: embrace of Giovanni being done via blood pot delivered form Cappadocius, and Nosferatu using pools of blood to ghoul vermin being the major ones.