Chackbox fields are stored as arrays similar to the way relationship fields are stored.
So your meta query would look something like this.
meta_query' => array(
'key' => 'music-taste', // name of custom field
'value' => '"' . $taste . '"', // matches exaclty "123", not just 123. This prevents a match for "1234"
'compare' => 'LIKE'
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