Why doesn't Anubis chase off the githyani?

To put it simply, no one knows.

The Guardian of the Dead Gods (it doesn't call itself Anubis anymore, and it is no longer a 'he') is an enigmatic being who does not explain its motivations to mortals. All mortals know is that sometimes you can mine a dead god, build a city on it, chop it into little bits and bring it into Sigil in pieces, and the Guardian of the Dead Gods will do nothing. Sometimes the Guardian of the Dead Gods will prevent you from even touching a dead god.

Obviously, there are forces and rationales at work other than simply preventing all dead gods from being harmed. Exactly what the Guardian of the Dead Gods is really up to, what pacts and agreements it has made, is not something it reveals. Perhaps it only guards certain dead gods whose surviving allies have agreed to supply it with the divine power it needs to continue its task. Perhaps some dead gods are more important, in the cosmic scheme of things, than others. Perhaps the Guardian of the Dead Gods can see into the future to some degree, and knows that some dead gods still have important roles to play in the fate of the multiverse, while others do not. Perhaps sometimes, it knows a dead god is fated to be destroyed utterly, and it merely waits to ensure this happens at precisely the right moment. Perhaps the Guardian of the Dead Gods simply can't be everywhere at once.

I, personally, like it too much to treat it simply as a monster the PCs have to fight every time they have to retrieve something from a god's corpse, and I like the idea of githyanki and other races building exotic cities on the corpses of long-dead powers too much to give up that aspect of the Astral Plane. The Guardian of the Dead Gods is more complicated and interesting than that, and the Astral Plane is more complicated and interesting than that.

If you get on the bad side of the Guardian of the Dead Gods, you are almost certainly screwed. It is far from toothless when it determines that it has to act. But the game doesn't need a brick wall for the PCs to run their heads against every time they want to do something cool. There are a lot of interesting stories that can be told involving Astral cities, godsblood-mining operations, and lost pieces of ancient divine corpses, and it'd be a shame to give any of those possibilities up because an unbeatable monster is pledged to destroy everyone who tries.

So that's not what the Guardian of the Dead Gods is. It is sometimes an obstruction to the PCs' plans. It is sometimes merely background, a cosmic sentinel who assures that not every deity is mined to nothing. It is sometimes a patron, of sorts, who can warn the PCs (as it does a few times in the adventure Dead Gods) when gods are returning to life, inspiring adventures. It is frustrating and unknowable, as a being of its stature should be. It is not predictable. The PCs can't simply summon it by finding a dead god and stabbing it (or doing anything else). If it does appear, it won't reappear every time they return to the area. It may resist allowing anyone to touch a god-corpse one day, but allow them to destroy it on another. It is above anything the PCs might do, or comprehend. It works on a greater scale, and sees things they do not. It is not a mere security device that goes off at predictable intervals. It is not at anyone's beck and call. Meeting the Guardian of the Dead Gods should be a rare, awe-inspiring event, something that only happens to the PCs on very special occasions.

The multiverse is a huge, wild, complicated, mysterious place, and the great entities who dwell in it can be just as confounding to mortal minds. This is how it should be. It'd be a shame if anything about them became routine.

There are a bunch of creative suggestions in my post above.

Perhaps the god upon which the githyanki built their main city is a god antithetical to Anubis.

Um. Sorry to bring up more counter-arguments, but if the one Tu'narath adventure is taken as canon (and if my memory serves- I lost Dragon #100) the god-isle Tu'narath is built on was implied to have been a good god.
There was some cavern in the isle where good PCs could commune with what was left of the god for what amounted to warm fuzzies and a bonus or two. Probably not a god of ghouls... or maybe I'm remembering it wrong. *shrugs*

Perhaps Anubus objects to the DESTRUCTION of a god, but considers what the githyanki do as merely RESHAPING the god's divine material, and therefore OK.

In Sigil, the Lady of Pain mostly only makes an appearance if she believes that either she or the city itself is threatened.

Inhabitants of the Cage, having lived there for generations, have developed a pretty good sense of what NOT to do, in order to avoid the Lady's wrath. This sense is generally more well-developed than that of visiting planars or Clueless.

Perhaps a similar situation exists in the Astral Plane. Having lived there for an incredibly long time, the githyanki (at least their leaders, those involved in mining godsblood, etc.) have a better sense than almost anyone of what they can and can't do with regard to god-isles without invoking Anubis' wrath. (This sense was probably acquired by having piked off Anubis repeatedly at some point...)

I think the Guardian is really there more to deal with players than with NPCs -- "No, you can't design a ritual to use the power of Bane to turn yourself into a greater deity." Note, however, that Vlaakith was trying to do something similar with the god-isle of Tu'narath in order to become divine!

Does the undertaker, the grave digger or the graveyard gardener remove each maggot from a corpse's body?

I don't think he cares if things live or feed on the dead gods, but grave robbers (stealing power, a corpse etc.) catch his attention.

How about this, did Anubis really set out to look after the dead gods?

It would be interesting to find him and see him eating a bit of godflesh!

Another idea is he is dieing, and really just waiting to die. Any intervention he does it just to pass the time (he may have hundreds of years left, but thats not much to him) Surely a god of death would know when he was gonna kick the bucket.