(Usage of 'Wikipedia' below should be understood as referring all the different language editions.)
The default appearance of MediaWiki is remarkably close to Wikipedia. For better or worse, many people intuitively associate the Vector skin with Wikipedia content and values. This makes the experience of viewing non-Wikipedia wikis slightly disorienting, especially when the content policy and editorial standards are dramatically different from Wikipedia's. It's not unreasonable to suspect that this hurts Wikipedia's reputation and credibility.
Traditionally the visual identity of individual projects has been asserted via the logo, but the logo is not prominently visible on the mobile site (and space constraints preclude it from being so) and it is not always visible on the desktop site (if you scroll past the top of the page, for example).
Wikipedia's visual identity should be distinct. It need not be obnoxiously and loudly distinct. It is probably sufficient to apply a subtle, non-default styling to a prominent UI element, like changing the color of the Vector sidebar to a slightly different shade of grey.
It is important for the software to remain free and freely reusable for third parties, and this includes the design. We don't need to withhold or conceal the CSS code; it'd be sufficient to make it non-default.