Your problem is not searching inside HTML links, but replacing inside what you already replaced in a previous loop. So: don't do multiple loops, instead, replace everything in one go. Build a regex with all search terms first, and do the substitution with a hash. Something like this:

$_ = <<'--';
Oh no, Anti-globalization activists are coming!
Globalization is rejected by...
--

use Regex::PreSuf;
%links = (
   'globalization' => '/encyclopedia/Globalization/index.html',
   'anti-globalization' => '/encyclopedia/Anti-Globalization/index.htm
+l'
  );
my $re = presuf(keys %links);

s/($re)/<a href="$links{lc $1}">$1<\/a>/gio;
print;
[download]

Result:

Oh no, <a href="/encyclopedia/Anti-Globalization/index.html">Anti-glob
+alization</a> activists are coming!
<a href="/encyclopedia/Globalization/index.html">Globalization</a> is 
+rejected by...
[download]

Regex::PreSuf is a module to build a regex out of a list of words. It'll escape metacharacters, so the resulting regex will always just do literal lookups.

Do note how I made the replacement case-insensitive, making the keys of the hash lower case, and doing the lookup with lc $1 — in addition to use of the /i switch.