Is there a way to override this so that things belonging to different data types are always not equal? Or is the rather verbose (ref($x) eq ref($y)) and ($x eq $y) the only way to do this?

Finally I fiddled it out, the perldoc for overload is not really the lightest weed to smoke. The Regexp object might be magical but still has an API to operate with.

So you may wanna try something like this, but I certainly don't recommend it for production use:

package Regexp;
 
use overload 
    q{cmp} => sub {
    return 1 if (ref($_[0]) ne ref($_[1]));
             # TODO: returning 1 is completely arbitrary
             # didn't know how to decide which ref is "bigger"
    return "$_[0]" cmp "$_[1]";
        },
    fallback => 1;
;
  
 
package main;
 
my $rx = qr/a/;
my $ry =qr/a/;
my $x="(?-xism:a)";
 
use Test::More 'tests' => 2;
cmp_ok( $rx, 'eq', $ry, '$rx eq $ry');
cmp_ok( $rx, 'ne', $x, '$rx ne $x');
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