Meta query for custom post type ignored in main query

Question

I looked through the interwebz but couldn't find a solution.

I am creating a website with custom post types where posts also include custom post meta (through ACF).

I am creating an archive file and I want to implement some filters (filter post by category and two different custom fields.

To even see the custom posts (called "mowcy") in category template I have added this snippet to my functions file:

Functions.php

function custom_post_type_cat_filter($query) {
   if ( !is_admin() && $query->is_main_query() ) {
      if ($query->is_category()) {
      $query->set( 'post_type', array( 'post', 'mowcy' ) );
      }
   }
} 

So now I uploaded a simple archive template to see how it works:

Archive.php

<?php 
get_header();
if ( have_posts() ) {
    while ( have_posts() ) {
        the_post();
          echo 'Title:' . get_the_title();
} else {
    echo 'Sorry, no posts';
}
get_footer();
?>

Now, here is where the problem starts:

If I specify the arguments in the code and use custom query to show custom posts with a specific custom fields value "EN" (an ACF field "languages" with multiple checkboxes for different languages), it works perfectly:

// Specify query parameters
$args = array(
    'post_type' => 'mowcy',
    'meta_query' => array(
        array(
            'key'     => 'languages',
            'value'   => '"EN"',
            'compare' => 'LIKE'
        )
    )
);
$the_query = new WP_Query( $args );
if ( $the_query->have_posts() ) // ... Beginning of the loop

However, if I print the same arguments to use in the URL (using http_build_query with $args), which looks like this:

post_type=mowcy&meta_query%5B0%5D%5Bkey%5D=languages&meta_query%5B0%5D%5Bvalue%5D=%22EN%22&meta_query%5B0%5D%5Bcompare%5D=LIKE

after reverting archive.php to use main query and URL parameters again, and using the above parameters, the meta_query is completely ommited from the query, and it just shows all of the posts of the custom type "mowcy". I can add a category parameter to URL and it works fine, but meta_query is still completely ignored.

What am I missing? Does query function ignore meta_queries on custom post types by default? How to fix this?

Also, as I said at the beginning, I plan to filter the posts by an additional second custom value too (so a second additional meta_query). Will this be an additional problem (while searching for a solution I have seen a few mentions that you need to manually merge two meta queries in such case)?

Thanks in advance for any kind of assistance.