This should do what you want:

#!/usr/bin/perl
use warnings;
use strict;

open OUT1, '>', 'GENEID.out' or die "can not create 'GENEID.out' $!";
open OUT2, '>', 'PROTID.out' or die "can not create 'PROTID.out' $!";

open FILE, '<', 'input.txt' or die "can not open 'input.txt' $!";

while ( my $line = <FILE> ) {
    select OUT1 if $line =~ /^>data_\d+\s+GENEID_\d+\b/;
    select OUT2 if $line =~ /^>data_\d+\s+PROTID_\d+\b/;
    print $line;
    }
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