@Pppery: could we use a video that isn't religious for the example image and code samples throughout the page? WMF properties have enough biases as it is, without adding a religious bias as well.
Topic on Extension talk:EmbedVideo
Ugh. (I just chose a video semi-randomly from c:Category:Media from YouTube that interested me, without paying much attention to its content)
Having a boring-looking video might be best anyways, since it'd discourage people from focusing on the video choice much.
It seems a little far-fetched to me that someone would make a claim of bias that the documentation for a video-embedding extension shows a video that happens to be religious.
Nevertheless, I would be willing to re-make this screenshot if someone else provides me with a link to a suitable creative-commons-licensed video on YouTube -- I don't feel like searching for a video that no one could possibly claim is objectionable myself.
@Pppery: This was an eye-opener to me too. I knew immediately from looking at it that this was footage of Stephen Anderson, the same radical Baptist preacher who has publicly exclaimed that he wants the government to execute homosexuals! I'm not accusing you of religious bias here, since you picked the video at random and you may not even have been aware of who Anderson is and his horrible beliefs, but we really shouldn't be including anything religious or political, especially something from a blatantly bigoted preacher, in technical documentation that has nothing to do with religion or politics. I ask that you please remove the image and find a different video example to use here. Even just an image depicting a man like this is highly inappropriate and can be taken both as highly offensive and that MediaWiki has a fundamentalist Baptist bias.
I repeat my offer from earlier. I'll remake the screenshot if somebody else provides a source creative-commons-licensed video.
Since you asked for a video example, I found this one in just a few minutes: from the Wikimedia Foundation's YouTube channel, look up "Knowledge Belongs to All of Us". This kind of video seems appropriate for technical documentation as an inoffensive and non-political example. (I tried to send you a video link here but the stupid filter disallowed it. It should know better; I've been active for years on several WMF projects through this account!)
OK, 
Pppery, eEveryone has a thing so asking someone to post a suitable video link vs just comment on yours is a good idea. That one would not bother me at all as I simply would not pay attention to it.
Admittedly I might be sensitized to it because I was raised in a Baptist church. That being said, I don't think we should say "it's just a hypothetical so there's no reason to bother", especially when we have so many potential alternatives. I'll probably poke around and see if I can find something else after a bit.