What's the best way to accomplish this: Hooks or CSS?

This question is pretty difficult to answer because it really depends on how this theme was built and what naming conventions they use on their files. Which is why you would need to provide more information but what I would do is first make a child theme if you have not already, then edit the file that is the archive for whatever page this is weather it is a category page, archive page or custom taxonomy. And where the structure of the code is set up add a php conditional to the class and echo out -fluid.

This is an example but it can look something like this:

<div class="container<?php if( is_page('example') ){ echo '-fluid'; } ?>">
<h1>Page Title</h1>
<p>This is a page,</p>
</div><!--container div-->

Now the conditional would all depend on where your template is in the template hierarchy. Note that this is just an example because I have very little information about this theme and how its set up to actually tell you how you can go about doing this. But this is just one way that I would go about adding a custom class depending on what page i'm on.

Hi guys. Thanks a ton for the feedback. The theme doesn't use hooks, unfortunately. I do use a child theme. The original was created by wpbeaverbuilder.

Richard Norby, the buddypress profile pages do not use pages in wordpress so I can't switch out the template using the UI. Assuming that is what you meant?

Lucas Santos, I like your idea. I tried to edit the page.php file in my child theme (which calls the container class) and put this in it but it keeps throwing the error below. Any idea why?

Parse error: syntax error, unexpected '}', expecting ',' or ';'

<?php get_header(); ?>

<div class="fl-content-full container<?php if( is_page("my-activity") ){ echo "-fluid" }; ?>">
    <div class="row">
        <div class="fl-content col-md-12">
            <?php if(have_posts()) : while(have_posts()) : the_post(); ?>
                <?php get_template_part('content', 'page'); ?>
            <?php endwhile; endif; ?>
        </div>
    </div>
</div>

<?php get_footer(); ?>