Should URL be case sensitive?

Depends on the hosting os. Sites that are hosted on Windows tend to be case insensitive as the underlying file system is case insensitive. Sites hosted on Unix type systems tend to be case sensitive as their underlying file systems are typically case sensitive. The host name part of the URL is always case insensitive, it's the rest of the path that varies.

According to W3's "HTML and URLs" they should:

There may be URLs, or parts of URLs, where case doesn't matter, but identifying these may not be easy. Users should always consider that URLs are case-sensitive.

All “insensitive”s are boldened for readability.

Domain names are case insensitive according to RFC 4343. The rest of URL is sent to the server via the GET method. This may be case sensitive or not.

Take this page for example, stackoverflow.com receives GET string /questions/7996919/should-url-be-case-sensitive, sending a HTML document to your browser. Stackoverflow.com is case insensitive because it produces the same result for /QUEStions/7996919/Should-url-be-case-sensitive.

On the other hand, Wikipedia is case sensitive except the first character of the title. The URLs https://en.wikipedia.org/wiki/Case_sensitivity and https://en.wikipedia.org/wiki/case_sensitivity leads to the same article, but https://en.wikipedia.org/wiki/CASE_SENSITIVITY returns 404.

The domain name portion of a URL is not case sensitive since DNS ignores case: http://en.example.org/ and HTTP://EN.EXAMPLE.ORG/ both open the same page.

The path is used to specify and perhaps find the resource requested. It is case-sensitive, though it may be treated as case-insensitive by some servers, especially those based on Microsoft Windows.

If the server is case sensitive and http://en.example.org/wiki/URL is correct, then http://en.example.org/WIKI/URL or http://en.example.org/wiki/url will display an HTTP 404 error page, unless these URLs point to valid resources themselves.