In your any and any_cr branches you are running any twice when you only need to run it once. If I fold the two together like this:

    any_fold => sub {
        while ( $data =~ /^(\d+) (\d+)/mg ) {
            next if any { $1 == $_ || $2 == $_ } @skip;
        }
        return 1
    },
    any_cr_fold => sub {
        while ( $data =~ /^(\d+) (\d+)/mg ) {
            my ( $c, $r ) = ( $1, $2 );
            next if any { $c == $_ || $r == $_ } @skip;
        }
        return 1
    },
[download]

I get these results:

any_cr       461/s        --        -13%      -58%      -62%      -68%
+      -76%
any_cr_fold  527/s       14%          --      -52%      -57%      -63%
+      -72%
any         1090/s      137%        107%        --      -11%      -24%
+      -43%
any_fold    1221/s      165%        132%       12%        --      -15%
+      -36%
ugly        1436/s      212%        172%       32%       18%        --
+      -25%
ugly_cr     1914/s      315%        263%       76%       57%       33%
+        --
[download]

Then, since I am on 5.42.0 and can use the new any keyword (suggested by ysth) by replacing your use of List::Util with:

no warnings "experimental::keyword_any";
use experimental 'keyword_any';
[download]

it gives these even better results:

              Rate       any  any_fold    any_cr      ugly any_cr_fold
+   ugly_cr
any         1037/s        --      -10%      -20%      -26%        -31%
+      -46%
any_fold    1152/s       11%        --      -11%      -18%        -23%
+      -40%
any_cr      1297/s       25%       13%        --       -7%        -14%
+      -32%
ugly        1399/s       35%       21%        8%        --         -7%
+      -27%
any_cr_fold 1506/s       45%       31%       16%        8%          --
+      -21%
ugly_cr     1914/s       85%       66%       48%       37%         27%
+        --
[download]

ugly_cr still wins but not by so much. But what's really interesting to me is that with List::Util, any_cr is much slower than any while with the new keyword, any_cr is slightly faster than any.