Their are five ways this can play out I can see. I'll try and order them as being ordered in likely hood from 1 (most likey) downwards.
1)They modify apu, bringing a new interpretation of the guy into a show which has turned to shit resulting in a unfunny pc apu for zombie simpsons.Which will cultivate resentment from long time simpson fans. , re-enforce the idea of certain groups are beyond satire and cultivates a canker of racial tension between 'white' murica and american indians by re-enforicing two contrasting narritives which cannot reconcile. Overall making the world a crapper place to live as white and indians collectively hate each other ever so slightly more.
2)Kill apu or vanish his ass more extreme version of option 1 most likely with far uglier reprecussions.
3)Nothing much is done but Apu is very slowly shunted into the background but since no-one watches the simpsons anymore no-one really cares. If we're really lucky tempers will cool so this can blow over.
4) The Simpsons staff grow a pair and show a willingness to critique the left like the did the right in their prime and tell Hari "To go fuck himself" or Rundi ko chod if you want to respect his culture. The media will jump on this and the whole thing will spiral into a massive shitfit but with both sides getting a lot nastyer and embittered. Nothing will be solved. Simular to 1 but with more talking heads.
5) We realize it's okay to love Apu warts and all and the not exceptional members of the Indian American community accept him as a legitimate character who fits well into the satirical subtext of the series. Kinda like mexicans did with speedy gonzales or the scotts did with Groundskeeper willie.
Pretty much all of these most likely include Hari's rapidly emerged rep as a misrable bastard.