You said "It is neither XML nor is it HTML", but at least the sample you showed is a valid XML document if parsed as a fragment, so that's what I did below. If your data is ever going to not be valid XML, you'd have to show an example of that. Mojo::DOM may still be able to parse it in that case while XML::LibXML is generally not very forgiving.

use warnings;
use strict;

# ##### Version with Mojo::DOM #####
# nicer API but less strict on parsing (useful for HTML)

use Mojo::DOM;
sub strip_tags_mojo {
    my ($str, $activetags) = @_;
    my %active = map {($_=>1)} @$activetags;
    my $dom = Mojo::DOM->new->xml(1)->parse($str);
    $dom->find('*')->grep(sub{ not $active{$_->tag} })->map('remove');
    my $text = $dom->all_text;
    $text =~ s/\s+/ /g;
    return $text;
}

# ##### Version with XML::LibXML #####
# generally a more verbose API but strict XML-compliant parsing
# (in the following I've tried to shorten the code quite a bit)

use XML::LibXML;
sub strip_tags_xml {
    my ($str, $activetags) = @_;
    my %active = map {($_=>1)} @$activetags;
    my $dom = XML::LibXML->new->parse_balanced_chunk($str);
    $active{$_->nodeName} or $_->parentNode->removeChild($_)
        for $dom->findnodes('*');
    my $text = $dom->textContent;
    $text =~ s/\s+/ /g;
    return $text;
}

# ##### Tests #####

use Test::More;
sub exception (&) { eval { shift->(); 1 } ? undef : ($@ || die) } # po
+or man's Test::Fatal

my $input = 'word1 <tag0> word2 <tag1>word3 word4</tag1> word5 </tag0>
+ word6 <tag2>word7 word8</tag2> word9 <tag3>word10</tag3> word11';
my @tests = (
    { in=>['tag0', 'tag1'], exp=>'word1 word2 word3 word4 word5 word6 
+word9 word11' },
    { in=>['tag3'], exp=>'word1 word6 word9 word10 word11' },
    { in=>['tag1', 'tag2', 'tag3'], exp=>'word1 word6 word7 word8 word
+9 word10 word11' },
);

plan tests => (@tests+1)*2;

for my $t (@tests) {
    is strip_tags_mojo($input, $t->{in}), $t->{exp};
    is strip_tags_xml($input, $t->{in}), $t->{exp};
}

ok not exception { strip_tags_mojo('foo <tag0> bar </tag1>') };
ok exception { strip_tags_xml('foo <tag0> bar') };
[download]

Update 2: Removed "Update" tags from the first paragraph for readability.