Apparently a not insignificant amount of people that watch anime don't care about anime opening themes at all. News to me.
I never skip an OP or an ED. Ever. Even if I hate it. It just feels like I'm being heretical and not getting the full experience if I do.
I do have a tendency to shift my attention to AnimeGAF during EDs lately, though.
It's a comedy show about four girls in a club whose activity is to joke around thinking up fresh "new ideas" for school clubs.
There's a fairly strict formula that episodes tend to follow: first they bring up the target club of the episode (say, a tennis club), then they discuss the existing tropes and cliches that tend to surround that club in real life, then they discuss the existing tropes and cliches that tend to surround that club in anime/manga, and finally each girl comes up with a bizarre idea to make the club more interesting. Then sometimes at the end of the episode they have a "practical activity" based on that club that is completely ridiculous.
In addition to being fairly meta in the nature of the discussions, since it's all about tropes and cliches, the show is also very prone to meta gags about itself, with the fourth wall often in various states of disrepair, the lyrics and animation of the OP being a parody of generic anime OPs, and in this second season they've started getting really into joking about cost-cutting measures, which results in bizarre animation gags like the one I screenshotted. Last week they spent the whole episode trying to move as little as possible.