Steps to reproduce the issue

1. Create a category
2. Create a menu-item linking to that category as blog for instance
3. Create a categories module with the same category and visible on the just created menu item
4. Do not enable SEF in your Joomla configuration

Expected result

The li element with the same category should have a 'active'-class

Actual result

Because of the difference in $_SERVER['REQUEST_URI'] and the ContentHelperRoute::getCategoryRoute in HTML characters, the li-element does not get the class 'active'.

Possible solution

File /modules/mod_articles_categories/tmp/default_items.php, replace the if-statement on ~ 13
Add:

$activeCatId = '';
if(JFactory::getApplication()->input->get('view') === 'category' )
{
    $activeCatId = JFactory::getApplication()->input->get('id');
}

And replace

<li <?php if ($_SERVER['REQUEST_URI'] == JRoute::_(ContentHelperRoute::getCategoryRoute($item->id))) echo ' class="active"';?>> <?php $levelup = $item->level - $startLevel - 1; ?>

with:

<li <?php if (!empty($activeCatId) && $activeCatId == $item->id) echo ' class="active"';?>> <?php $levelup = $item->level - $startLevel - 1; ?>