2021 Solution

a[href]:not(:where(
  /* exclude hash only links */
  [href^="#"],
  /* exclude javascript only links */
  [href^="javascript:" i],  
  /* exclude relative but not double slash only links */
  [href^="/"]:not([href^="//"]),
  /* domains to exclude */
  [href*="//stackoverflow.com"],
  /* subdomains to exclude */
  [href*="//meta.stackoverflow.com"],
)):after {
  content: '';
}

<strong>Internal sites:</strong>
<br>Lorem <a href="http://stackoverflow.com">http://stackoverflow.com</a> ipsum
<br>Lorem <a href="/a/5379820">/a/5379820</a> ipsum
<br>Lorem <a href="//stackoverflow.com/a/5379820">//stackoverflow.com/a/5379820</a> ipsum
<br>Lorem <a href="http://stackoverflow.com/a/5379820">http://stackoverflow.com/a/5379820</a> ipsum
<br>Lorem <a href="https://stackoverflow.com/a/5379820">https://stackoverflow.com/a/5379820</a> ipsum
<br>Lorem <a href="https://meta.stackoverflow.com/">https://meta.stackoverflow.com/</a> ipsum
<br>Lorem <a href="ftp://stackoverflow.com">ftp://stackoverflow.com</a> ipsum

<br><br>
<strong>External sites:</strong>
<br>Lorem <a href="ftp://google.com">ftp://google.com</a> ipsum
<br>Lorem <a href="https://google.com">https://google.com</a> ipsum
<br>Lorem <a href="http://google.com">http://google.com</a> ipsum
<br>Lorem <a href="https://www.google.com/search?q=stackoverflow">https://www.google.com/search?q=stackoverflow</a>
<br>Lorem <a href="//www.google.com/search?q=stackoverflow">//www.google.com/search?q=stackoverflow</a>

<br><br>
<strong>Other anchor types</strong>
<br>Lorem <a>no-href</a> ipsum
<br>Lorem <a href="#hash">#hash</a> ipsum
<br>Lorem <a href="javascript:">javascript:</a> ipsum

2014 Solution

Using some special CSS syntax you can easily do this. Here is one way that should work for both the HTTP and HTTPS protocols:

a[href^="http://"]:not([href*="stackoverflow.com"]):after,
a[href^="https://"]:not([href*="stackoverflow.com"]):after {
  content: '';
}