So far I've tried it myself this way:

sub filter {
   die 'Error: no fields to filter through' if (@_ < 2);
   my $response = shift;
   my @fields;
   foreach my $a (0..$#_) {
      $fields[$a]= shift; }
   
   if (ref $response eq 'ARRAY') {
      my @response = @$response;
      my @filtered_responsearr;
      my %filtered_response;
      
      foreach my $ref (@response) {
         my %response = %$ref; 
           foreach my $field (@fields) {
              $filtered_response{$field}=$response{$field};
              }
              
              push @filtered_responsearr, %filtered_response;
              
     }
     return \@filtered_responsearr;
    }
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which returns an array of all the fields, like ['name','foo','id','bar','name','foo2','id','bar2']
But I don't need an array of all the fields, I need an array of hashes, because I have to work with the hashes afterwards

You want to push a hash reference and not a hash:

push @filtered_responsearr, \%filtered_response;
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Your code can be greatly simplified in some other places:

   my $response = shift;
   my @fields;
   foreach my $a (0..$#_) {
      $fields[$a]= shift; }
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can be rewritten as a single assignment:

my( $response, @fields ) = @_;
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Likewise, copying the elements of %response into the filtered response can be done using a hash slice instead of the loop:

@filtered_response{ @fields } = @response{ @fields }
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%filtered_response is declared only once in the function call, so every reference to it will be identical. { %filtered_response } would work, but it would be better to move the declaration of %filtered_response inside the for loop.

Or, with a recent enough version of perl, you can use a pairwise slice: push @filtered_responsearr, { %response{ @fields } };.
With a postfix dereference: push @filtered_responsearr, { $res->%{ @fields } }

Edit: I added the missing { } in the last line, to have a hash reference and not pairs of values.

Wow, thanks for the tips, didn't know about hash slice. I'm just getting started so please forgive me my noobness. I tried what you said but it just gave me the same hash over and over, but Eily's answer solved that as well. Thanks to you both!

   foreach my $a (0..$#_) {
      $fields[$a]= shift; }
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Avoid using $a and $b as variables, give them other names ;) .
perlvar -> $a, $b