아래 코드를 찾아서

<?php if($board->use_category == 'yes'):?>
<!-- 카테고리 시작 -->
<div class="kboard-category category-mobile">
    <form id="kboard-category-form-<?php echo $board->id?>" method="get" action="<?php echo $url->toString()?>">
        <?php echo $url->set('pageid', '1')->set('category1', '')->set('category2', '')->set('target', '')->set('keyword', '')->set('mod', 'list')->toInput()?>
        
        <?php if($board->initCategory1()):?>
            <select name="category1" onchange="jQuery('#kboard-category-form-<?php echo $board->id?>').submit();">
                <option value=""><?php echo __('All', 'kboard')?></option>
                <?php while($board->hasNextCategory()):?>
                <option value="<?php echo $board->currentCategory()?>"<?php if(kboard_category1() == $board->currentCategory()):?> selected<?php endif?>><?php echo $board->currentCategory()?></option>
                <?php endwhile?>
            </select>
        <?php endif?>
        
        <?php if($board->initCategory2()):?>
            <select name="category2" onchange="jQuery('#kboard-category-form-<?php echo $board->id?>').submit();">
                <option value=""><?php echo __('All', 'kboard')?></option>
                <?php while($board->hasNextCategory()):?>
                <option value="<?php echo $board->currentCategory()?>"<?php if(kboard_category2() == $board->currentCategory()):?> selected<?php endif?>><?php echo $board->currentCategory()?></option>
                <?php endwhile?>
            </select>
        <?php endif?>
    </form>
</div>

<div class="kboard-category category-pc">
    <?php if($board->initCategory1()):?>
        <ul class="kboard-category-list">
            <li<?php if(!kboard_category1()):?> class="kboard-category-selected"<?php endif?>><a href="<?php echo $url->set('category1', '')->set('pageid', '1')->set('target', '')->set('keyword', '')->set('mod', 'list')->tostring()?>"><?php echo __('All', 'kboard')?></a></li>
            <?php while($board->hasNextCategory()):?>
            <li<?php if(kboard_category1() == $board->currentCategory()):?> class="kboard-category-selected"<?php endif?>>
                <a href="<?php echo $url->set('category1', $board->currentCategory())->set('pageid', '1')->set('target', '')->set('keyword', '')->set('mod', 'list')->toString()?>"><?php echo $board->currentCategory()?></a>
            </li>
            <?php endwhile?>
        </ul>
    <?php endif?>
    
    <?php if($board->initCategory2()):?>
        <ul class="kboard-category-list">
            <li<?php if(!kboard_category2()):?> class="kboard-category-selected"<?php endif?>><a href="<?php echo $url->set('category2', '')->set('pageid', '1')->set('target', '')->set('keyword', '')->set('mod', 'list')->tostring()?>"><?php echo __('All', 'kboard')?></a></li>
            <?php while($board->hasNextCategory()):?>
            <li<?php if(kboard_category2() == $board->currentCategory()):?> class="kboard-category-selected"<?php endif?>>
                <a href="<?php echo $url->set('category2', $board->currentCategory())->set('pageid', '1')->set('target', '')->set('keyword', '')->set('mod', 'list')->toString()?>"><?php echo $board->currentCategory()?></a>
            </li>
            <?php endwhile?>
        </ul>
    <?php endif?>
</div>
<!-- 카테고리 끝 -->
<?php endif?>

아래 코드로 교체한 후 테스트 해보시겠어요?

<?php if($board->use_category == 'yes'):?>
<!-- 카테고리 시작 -->
<div class="kboard-category">
    <form id="kboard-category-form-<?php echo $board->id?>" method="get" action="<?php echo $url->toString()?>">
        <?php echo $url->set('pageid', '1')->set('category1', '')->set('category2', '')->set('target', '')->set('keyword', '')->set('mod', 'list')->toInput()?>
        
        <?php if($board->initCategory1()):?>
            <select name="category1" onchange="jQuery('#kboard-category-form-<?php echo $board->id?>').submit();">
                <option value=""><?php echo __('All', 'kboard')?></option>
                <?php while($board->hasNextCategory()):?>
                <option value="<?php echo $board->currentCategory()?>"<?php if(kboard_category1() == $board->currentCategory()):?> selected<?php endif?>><?php echo $board->currentCategory()?></option>
                <?php endwhile?>
            </select>
        <?php endif?>
        
        <?php if($board->initCategory2()):?>
            <select name="category2" onchange="jQuery('#kboard-category-form-<?php echo $board->id?>').submit();">
                <option value=""><?php echo __('All', 'kboard')?></option>
                <?php while($board->hasNextCategory()):?>
                <option value="<?php echo $board->currentCategory()?>"<?php if(kboard_category2() == $board->currentCategory()):?> selected<?php endif?>><?php echo $board->currentCategory()?></option>
                <?php endwhile?>
            </select>
        <?php endif?>
    </form>
</div>
<!-- 카테고리 끝 -->
<?php endif?>