I think "this software is for personal use only" is the main (only?) GPL incompatible parts of the App Store terms. I don't know if it's a possible outcome, but I wonder if there's some way to force iOS to be an OS where you can run any programme (i.e. no App Store needed), if there is GPL software. This is clearly not something Apple want, so they may be trying to nip that problem in the bud by setting things up to stop GPL. I believe some sort of Microsoft app store explicitly bans GPL.
Apple do officially care, and they only officially allow things in that match their rules. If you told Apple that the software was GPL, they would probably care and pull it.
The reason VLC was there for long was because Apple clearly don't check things in the App Store very much (examples like this, and various scammy apps, and pirated software back this up). However once (one of) the copyright holders noticed it, they informed Apple that Apple was distributing copyright infringing software, and Apple promptly acted.
GPL software on the iOS App Store is about as legal as copying DVDs of Hollywood films and selling them yourself, or copying someone else's closed source software and uploading it to the App Store.
Remember, GPL software is often based on other GPL software that someone else wrote, and released to you under certain terms (the GPL). To distribute it via the App Store goes against the spirit and letter of those terms. It should be clear why some developers are annoyed about people who do that.