You could use a character class and a back reference instead of alternation.

my $string = qq{var1='1' var2="2" var3="3"};

while ( $string =~ /(\w+)=(['"])(.*?)\2/g) {
    print "$1 = $3\n";
}
[download]

use 5.010_000;

while ( $string =~ /(?<variable>\w+)=(?<delim>['"])(?<value>.*?)\k<del
+im>/g) {
    say "$+{variable} = $+{value}";
}
[download]