An issue is that push @{ $data{$taxon} }, $3; does not make sense - you intimate that data is a hash of hash, but you are using it as a hash of array in that statement.

Without more information telling us what you want to do with the data it's not clear if the data structures you are generating are appropriate. Consider the following sample however:

use strict;
use warnings;

my $file1 = <<FILE;
dna:
species_1  ACCATGATACGATG
species_2  GGTTTCGACGCAGA
species_3  GGACTCAGCGACTA
FILE

my $file2 = <<FILE;
morph:
species_1  001001010201001001
species_2  002010200210120201
species_4  001001110000000101
species_5  111001001001000201
FILE

my %data;
my $dnaLen = 0;
my $morphLen = 0;

open IN, '<', \$file1 or die "Failed to open file1: $!";
while (<IN>) {
    next unless /(^\w+)\s+(\w+)/;
    $data{$1}{dna} = $2;
    $dnaLen ||= length $2;
}
close IN;

open IN, '<', \$file2 or die "Failed to open file2: $!";
while (<IN>) {
    next unless /(^\w+)\s+(\w+)/;
    $data{$1}{morph} = $2;
    $morphLen ||= length $2;
}
close IN;

die "No dna data found" unless $dnaLen;
die "No morph data found" unless $morphLen;

for my $species (sort keys %data) {
    $data{$species}{dna} ||= '?' x $dnaLen;
    $data{$species}{morph} ||= '?' x $morphLen;
    print "$species: $data{$species}{dna}$data{$species}{morph}\n";
}
[download]

Prints:

species_1: ACCATGATACGATG001001010201001001
species_2: GGTTTCGACGCAGA002010200210120201
species_3: GGACTCAGCGACTA??????????????????
species_4: ??????????????001001110000000101
species_5: ??????????????111001001001000201
[download]

which uses a hash of hash where the primary key is the species and the secondary key is morph or dna.