You could just rejoin your strings after spliting and sorting and then compare them:

#! perl -slw
use strict;

sub reorder {
    my $string = shift;
    return join ',', sort{ $a cmp $b } split ',', $string;
};;

my $string1 = '~cake,pastry';
my $string2 = 'pastry,~cake';
my $string3 = 'cake,pastry';

print "$_->[ 0 ] eq $_->[ 1 ]",
    reorder( $_->[ 0 ] ) eq reorder( $_->[ 1 ] )
        ? ' match '
        : ' dont match'
    for [ $string1, $string2 ],
        [ $string1, $string3 ],
        [ $string2, $string3 ];
__END__

[ 8:16:14.39] P:\test>junk2
~cake,pastry eq pastry,~cake match
~cake,pastry eq cake,pastry dont match
pastry,~cake eq cake,pastry dont match
[download]

Not hugely efficient, but probably not too bad if there are only a few elements in your strings.