This (is)- my first string, is not a regular expression. It's just a string. But when you wrap it in an m// operator, you're telling Perl it's a regular expression. Within regular expressions, parenthesis have meaning. In fact just about every printable non-word character on your keyboard has meaning to the regex engine. So let's look at what you're asking Perl to validate:

use 5.012_002;
use strict;
use warnings;
use YAPE::Regex::Explain;

my $var1 = "This (is)- my first string";
my $var2 = "This (is)- my first string";

say YAPE::Regex::Explain->new($var2)->explain();
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And the output:

The regular expression:

(?-imsx:This (is)- my first string)

matches as follows:
  
NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  This                     'This '
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    is                       'is'
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
  - my first string        '- my first string'
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------
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So you're asking Perl if "This (is)- my first string" matches "This is- my first string" (the parens are getting interpreted as 'something else' within the regular expression. You have a few options. One is to pass your second string through quotemeta. Another is to simply do a direct comparison using 'eq', rather than a regexp match.