There are a raft of techniques that clean your code up. The first is to throw the CSV file parsing over to a tool built for the job (Text::CSV). After that tossing the eval stuff aside and using a match function cleans up the rest of the code something wonderful. Consider:

#!/usr/bin/perl
use warnings;
use strict;
use Text::CSV;
use 5.010;

my $ops = <<OPS;
column    relationship    value    num_or_string    filter_or_append  
+  order
a    <=    0.3    num    filter    1
b    eq    abc    string    append    3
c    <=    0.3    num    filter    2
OPS

my $csv = Text::CSV->new ({sep_char => "\t"});
open my $opsIn, '<', \$ops or die "Cannot open file: $!";

$csv->column_names($csv->getline($opsIn));
my @ops = @{$csv->getline_hr_all($opsIn)};
close $opsIn;

my %filtColumns = map {$_->{column} => 1} @ops;
my @inColumns = @{$csv->getline(*DATA)};

if (grep {! exists $filtColumns{$_}} @inColumns) {
    die <<DIE;
COLUMN NAME DOES NOT EXIST. CHECK FILTER FILE FOR ANY POSSIBLE ERRORS 
+AND RE-RUN
PROGRAM. PROGRAM WILL NOW TERMINATE.

DIE
    exit 0;
}

$csv->column_names(@inColumns);
$csv->combine(@inColumns);
print  $csv->string (), "\n";

while (my $line = $csv->getline_hr(*DATA)) {

    next if grep {! match($line, $_)} @ops;

    $csv->combine(@{$line}{@inColumns});
    print  $csv->string (), "\n";
}


sub match {
    my ($line, $filter) = @_;
    my %fields = %$filter;
    my $value = $line->{$fields{column}};
    
    given($fields{relationship}) {
        when ('<=') {return $value <= $fields{value}}
        when ('eq') {return $value eq $fields{value}}
        default {
            die "match can't handle $fields{relationship} operator\n";
        }
    }
}


__DATA__
a    b    c
0.2    abc    0.3
0.1    abd    0.3
0.4    abe    0.2
0.1    abc    0.5
0.7    abt    0.7
0.1    abd    0.8
[download]

Prints:

a    b    c
0.2    abc    0.3
[download]

No doubt I've missed the significance of some of your code (I've not followed along on your whole journey to this point), but the sample code above should give you a good starting point for further development.