You can achieve the OR relation using the tax_query argument like so:
$query->set( 'tax_query', array(
'relation' => 'OR',
array(
'taxonomy' => 'category',
'terms' => array( 2, 3 ),
),
array(
'taxonomy' => 'post_tag',
'terms' => array( 10, 13 ),
),
) );
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