You are presuming it has to be homebrew.
No. I "presume" nothing. I am acknowledging reality. This IS a homebrew. I homebrewed it. Made it up whole cloth from my own preferences and opinions on what would be enjoyable [for me and hopefully others] in a game of D&D.
You think something ELSE would be enjoyable? That's AWESOME! You are welcome to take this document and make whatever changes you want/think will work better at your table. Have a great time.
As in every single published D&D setting it makes sense in.
I don't follow what this means.
So basically you have never heard of Ravenloft (no Orcs or Goblins unless they are individuals who wound up there by accident),
I've heard of it. Don't play in it. Don't care about it. If you do, take something else and put it in their place. For what I know of Ravenloft, might I suggest Vampires and Werewolves.
Dark Sun (no Orcs or Goblins), Dragonlance (No Orcs),
Yeah. *shrug* So? I'm not writing this for either of those specific settings. If I did/do, the cover will read
"Steel Dragons' Guide to [Specific Setting] [Whatever Class/Race/Topic it is] for 5e."
Planescape (Too cosmopolitan for there to be any racial animosity),
This is ridiculous and incapable of being true. Just because the feature is there, doesn't mean anyone
has to act on those impulses. In a place like Planescape (which I also do not like/have never played in), rest assured there is a TON of racial animosity...folks just know they can't always act on it without consequences. These abilities (well, the gnome's does a little, but for dwarves...) don't say the PC MUST attack Orcs and Goblins, Giants or Ogres. Just that they get xuyz benefits if they do. [And a P.S. reply to your last post, the dwarven ability does, specifically, call out the dwarf's AC bonus against Giants and ogres as applying to all Huge or larger creatures].
Eberron (Dwarfs have no particular beef with either Orcs nor Goblins),
Excellent example of one of my many problems with/why I don't like or play in Eberron.
Al-Quadim (There wars between races there).
Again, specific settings are/will be specific. They have their own rules and norms and tropes. That's great...for those settings. There is no reason I (or any designer) need to write to achieve/satiate each and every possible setting a person can play in. That's just a good way to drive one's self nuts.
Quite frankly, the number of settings in which it makes no sense for Dwarfs to be trained specifically to murder those select particular races greatly outnumber those where it makes any sense.
You mean besides Greyhawk, FR, Mystara, and pretty much every "default"/typical/traditional fantasy setting [published and homebrewed] ever? Yes, if you want to discount those innumerable settings, the number of settings in which it makes sense is "greatly outnumbered."
Moreover, it frankly says something about a person who would imply that a supposedly "good" race would be universally physiologically or culturally necessarily trained to genocidally exterminate members of a different race to the degree that every single last member would be specialized in killing them.
OK. If you want to throw around implications of some kind of racism/genocide motivations, you are welcome to leave this thread (or any I ever write). I'm not putting up with that nonsense in my creative threads.
1) It's not "every single" member of this race. It's the adventuring warrior guys. The guys who would be fighting them. As always, from the dawn of the game, when it comes to demi-/non-humans (and in most cases, the humans as well) the "PC" version of the race is not the "everyman/commoner" of the race.
2) It says NOTHING about "the person", i.e.
ME, other than I prefer, expect, and enjoy a world of GOOD and EVIL as real forces battling it out in/for the world. I want my dwarves, elves, and halflings to be (for the overwhelming most part) GOOD people, fighting for good things/ends. I want orcs, goblins, ogres, trolls, [most] giants, etc... that are innately EVIL people, fighting for evil things/ends. It's a trope. It's the original "fantasy world" trope. It spans any number of versions of D&D, clones, and other fantasy games...and I like it.
That's what it "says."
3) But to take that and make the leap to "it says something about [me]" that good guys are going to want to exterminate/put an end to bad guys? What's that say about the person making the leap? What it says about me, as far as I'm concerned: I want GOOD to TRIUMPH over evil. Crazy idea! I know.
And to hopefuly stop the tangent before it starts, before you retort with the ridiculous political correctness "everything's a grey-area so we don't ruffle anyone's feathers" that are so en vogue these days, "Who gets to decide what's Good/Evil?"
The DM. That's who. It's that simple. It's a fantasy game of make-believe magic and elves, not a 21st Century Morality dissertation.
4)...And a race of short bearded tough vastly outnumbered guys, periodically battling overwhelming odds, probably have some kind of special skill/expertise/training [or magic] that has allowed them and their culture/civilizations to survive for centuries.
But, as I said-- it is an easy fix. You just say that this particular class specializes in fighting whatever happens to be the thing that generally poses the greatest threat to their clan and open it up for the player and DM to decide what sort of creature that might be rather than imposing something and suggesting that it requires a houserule to a houserule to fix this?
And the fact that there are people out there that would "need" that, or expect it or think a document "should be", explained/written out for them makes me weep for the D&D gaming community. I suppose, if I were trying to
sell this/these, I would make the verbiage more general to appeal to the most/widest possible audience. But I'm [currently] not.
I still have nostalgic notions about the Known World/Mystara setting -- I still own copies of all the Gazetteers 
