Since characters in square brackets happen to be character classes in regexes, why not use them as such!?

use strict;
use warnings;
use Algorithm::Loops qw(MapCarE);

MapCarE {
    my ($s, $t) = @_;
    my $x= $t =~ /$s/ ? '~' : '!';
    print "$t $x~ $s\n";
}
[shift =~ /\[\w+\]|\w/g],    # split source into chars or char classes
[split //, shift];        # split target into chars
[download]

D:\temp>mm [TCG]GGGG[AT] AGGGGC
A !~ [TCG]
G ~~ G
G ~~ G
G ~~ G
G ~~ G
C !~ [AT]

D:\temp>mm [TCG]GGGG[AT] TGGGGC
T ~~ [TCG]
G ~~ G
G ~~ G
G ~~ G
G ~~ G
C !~ [AT]
[download]

Using Algorithm::Loops just for the convenience to iterate over two lists at once without distracting from the main point.