I think any humor that's to be mined from this comes from curiosity at seeing how one may look as another ethnicity and not at humor from "lol that ethnicity looks funny."
The pic posted in the OP is fascinating to me and I find it genuinely impressive how technology found in casual apps like these can produce fairly natural looking results. On the most basic level, it's no different from utilizing the filters that make you look younger, older, or a different sex.
It's an interesting curiosity precisely because it's modifying a visage you've known and seen in its "normal" state.
People can obviously take these images and use them for poor reasons, but I think the technology at play is super fascinating.
This reminds me of a factual TV programme here in the UK from a few years ago. A black guy and a white guy were made up to look white and black retrospectively. (I think it might have based on an American book from the 1950s.)
They then went about their daily lives to see if their 'race' affected how they were treated or how they viewed the world.
The black guy, who was pretending to be white, ended up at a far right march. I think he said he ended up feeling sorry for the people there.
The white guy, pretending to black, went to a dinner party where everyone else was actually black. Even though the guests knew this, I think one asked him what part of Africa his family were from and he had to remind her he was white.
Ah, I've found a video of the series. It's from 2002.
From my European point of view, the concept of race is something that the US should strife to abolish in favor of the concept of ethnicity. Anything that helps normalize the idea that people are inherently different from one another and that a distinction based on skintone is all that is needed because no other differences in genetic make-up exist even among people that share the same color, is not a good thing to exist either.
I don't use FaceApp. I don't even know what it is, but apparently this is new and I think I'm kinda spent. A thread on FB popped up with people posting how the app took their pics and made them Black, Asian, and what have you.