How customisable is WordPress?

I would definitely go with Extremely customizable here.

In my 7-8 years of work with WordPress, I have created a lot of custom stuff over the years, that on first glance was not looking like a possibility in the CMS but they actually have actions or hooks. I still get surprised sometimes that there is a filter or function “for that”. But what is “that”? Let me drop a quick list of possible scenarios you might get in to with WordPress if you are a developer:

• With HTML, CSS and PHP knowledge you will be able to make anything design-wise for your project. You can also level up the game by using Twig and Blade integrations.
• The Custom Post Type and Taxonomies can be used to create different content types and manage their slug structures easily. The way you need it to be.
• Rewriting permalinks structures
• Customize Theme and Plugin functions by disabling them and hooking our own.
• Custom menu walkers for changing the outputs of WP Menus to Front End
• Decent REST API supporting custom endpoints making is great for an easy UI editable database.
• The Customizer! The idea of this one is that we can write for a UI that will make a change to the theme appearance through a Live view window.
• Child Themes is a technique which is used to overwrite theme files without changing the theme itself.

WordPress has been used thousands of times (or more) for Affiliate Websites, Portfolios, Shops, Booking Websites, Real Estate, Directories, Forums, Classifieds, Knowledgebase (With a REST API). Some sites created with WordPress are: TechCrunch, PlayStation.Blog, The Official Star Wars Blog, BBC America, MTV News, Facebook Newsroom

Note that I speak for WordPress as a CMS and not a theme you might be using.

Have a great one!