Precompiling the regexes should provide a speedup and using List::MoreUtils::any() may do if the chance of a match is good since the test will shortcut on success. Naturally you will benchmark;-)

use List::MoreUtils qw(any);

open my $OUT, '>', 'Result_file.txt' or die "Cannot create file: $!\n"
+;
open my $IN,  '<', 'Input_file.dat'  or die "Cannot read file: $!\n";

# precompile the regexes.
@tag_rx = map {qr/$_/} @tag;

while ( my $data = <$IN> ) {
    print $OUT $data if any { $data =~ /$_/ } @tag_rx;
}
close $IN;
close $OUT;
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