The print method expects an array reference, not a hash reference:

use v5.12;
use warnings;

use Text::CSV_XS;

my $csv = Text::CSV_XS->new ({
    binary    => 1,
    sep_char  => ";",
    eol       => $/,
    auto_diag => 1,
    });

my @fields = qw( ID NAME INDICATOR VALUE CI_LOW CI_HIGH );
$csv->print (*STDOUT, \@fields);
say  '';

my @columns = @{$csv->getline (*DATA)};
$csv->column_names (@columns);

while (my $hr = $csv->getline_hr (*DATA)) {
    # my @nr = @{$hr}{'ID'};
    $hr->{ID} =~ s/12/Sun/g;
    $hr->{ID} =~ s/17/Moon/g;
            
    $csv->print (*STDOUT, [ map { $hr->{$_} } @columns ]);
    }
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Much easier to read and much faster too would be to use bind_columns

my @fields = qw( ID NAME INDICATOR VALUE CI_LOW CI_HIGH );
$csv->print (*STDOUT, \@fields);

my @columns = @{$csv->getline (*DATA)};
my %rec;
$csv->bind_columns (\@rec{@columns});
while ($csv->getline (*DATA)) {
    $rec{ID} =~ s/12/Sun/g;
    $rec{ID} =~ s/17/Moon/g;
            
    $csv->print (*STDOUT, [ @rec{@columns} ]);
    }
[download]

update: I stripped the data sections from the code as they are identical to those in the OP and reduced the second example to show only the changed part.