Well unfortunately, in my case it was not the WordPress customizer that was the problem, it was my theme (Avada). It has it’s own options for Event Calendar customization, and they were overwriting the plugin styles.
I sadly had to add a couple of !important tags to category.css.php, which is naughty, I know! It did the trick, and I will note to fix it upon updating the plugin in the future, but this fixes my problem in the short term.