How to hide posts of a specific custom category in WordPress?

I think you should be able to do this with a tax_query in your $args.
I could not test this, and I also dont know how the query behaves with a meta and tax query in one.

But I would start with testing something like this:

'tax_query' => array(
    array(
        'taxonomy' => 'event_category', // the used taxonomy
        'field'    => 'term_id', // use ID or slug
        'terms'    => array( 2136 ), // term ID to exclude
        'operator' => 'NOT IN', // "NOT IN" to exclude?, default "IN"
    ),
),

Some more infos in the offical codex.