“I’m proud of what we do on the show,” Groening told USA Today. “And I think it’s a time in our culture where people love to pretend they’re offended.”
Pretend they are offended ... is not what the people who are offended seem to have been doing. No, it seems people are genuinely offended. The accounts of how and when "thank you, come again" began to be appropriated as a kind of racial/ethnic slur has been discussed in enough places I don't feel like dredging that up. If you want to find that writing it's not too difficult to find. This is something where giving my mixed lineage of American Indian and white ancestry I'm frankly willing to have some sympathy for those who are annoyed by the frequency of ethnic and racial stereotypes in popular culture. I don't like to listen to the radio as a matter of course in day job life but coworkers like to listen to the radio and, well, I hate GEICO ads. Most attempts at wit in GEICO ads are glib and stupid and one of the most annoying ones was the one about the "really charming snake charmer". There are times when I enjoy humor and there are a lot of times where, honestly, I don't. It's not just Mere Orthodoxy writers who in their attempts at wit come off as witless, it's also just about every GEICO ad that includes "surprising" (which is all of them).
On the other hand ... nobody truly familiar with animation as an art form and an industry can take complaints about a person like Azaria voicing a character like Apu as prima facie evidence of racism or stereotyping without any regard for content or context. Yes, Apu can be thought of as a stereotype but humor traffics in stereotypes and can be distilled to laughing with or laughing at. Since I like to read sermons by Richard Sibbes and think the Puritans have become too lazy and popular a stereotypical scapegoat for social and ideological problems that pervade contemporary American culture I think there's room for being, in select contexts, a humorless Puritan.
Even the bromide about the dangers of the Puritan legacy is itself an appeal to an egregious stereotype. John O'Sullivan, the one who articulated Manifest Destiny was not, for instance, a Puritan. A lot of the legacy of Puritanism that is considered terrible can be pinned on Calvinism rather than on postmillennialism and if we have to pick one of these two that goes farther in explicating the negative impact of American colonialist religious ideology the postmillennialism is a far better option than what is at this point a mere five-point soteriology in favor of monergism in Anglo-American religious thought in just the Christian subset of Anglo-American religion. That doesn't mean a comparably dangerous and facile sense of personal destiny can't be dredged up from a post-Joseph Campbell form of Jungianism in popular culture colloquially known as "the hero's journey".
But at a more practical level, as I've noted before, if the problem is that Apu is not voiced by an east Indian that's a misunderstanding about animation and voice acting. Phil LaMar doesn't have to be Japanese to do a magnificent job voicing Samurai Jack any more than Mae Whitman has to be a Pacific Islander to do a magnificent job voicing Katara in The Last Airbender series. Groenig is in many respects on solid ground being dismissive of a controversy that has emerged after his creation has been on television for longer than many people who watch the show have even been alive. That doesn't mean his dismissal can or should seem altogether justified. It's possible for Groenig's response to be irresponsibly glib at one level and perfectly understandable at another. It's also possible to take seriously the concerns people have about racial stereotyping in a cartoon character like Apu seriously at one level (i.e. the case that when Apu is the "only" presentation of a type that that type can be negative) and not seriously at another (as more entertainers who are actually east Indian have roles in the entertainment industry there's room for development and there's problems of misunderstanding and misrepresenting the nature of animation as a field if the rules of purity and presentation for live-action representation are applied to an art form in which you never have to look like the character you play in order to voice a character, something I'm sure Peter Cullen has been grateful for every day of the last forty odd years he's voiced Optimus Prime).