Is it possible to remove some things from pages such as Shop By Category?

I think these sections might be part of your theme.

That’s what I was thinking too, but I can’t seem to find it in the theme settings. We are currently using Storefront if that helps at all.

Look in appearance > widgets if this is the homepage.

They are part of the homepage theme, so I added the following code to functions.php

add_action( 'homepage', 'storefront_remove_hooks' );
function storefront_remove_hooks() {
	remove_action( 'homepage', 'storefront_featured_products', 40 );
	remove_action( 'homepage', 'storefront_recent_products', 30 );
	remove_action( 'homepage', 'storefront_popular_products', 50 );
	remove_action( 'homepage', 'storefront_on_sale_products', 60 );
}

The various options you can remove are:-

* Functions hooked in to homepage action
*
* @hooked storefront_homepage_content – 10
* @hooked storefront_product_categories – 20
* @hooked storefront_recent_products – 30
* @hooked storefront_featured_products – 40
* @hooked storefront_popular_products – 50
* @hooked storefront_on_sale_products – 60
* @hooked storefront_best_selling_products – 70
*/