First

1. If you're only expecting 1 category there's no need to load them all to just get the first
2. Inject the dependency if doing the logic in a controller
3. The reason why your extension method GetCategories doesn't work is it needs to be in a separate static class

Although you don't need GetCategories I have rewritten including the GetCategories extension if you need it for the future

public class ParallaxNavigationBlockController : BlockController<ParallaxNavigationBlock>
{
    private readonly CategoryRepository _categoryRepository;

    public ParallaxNavigationBlockController(CategoryRepository categoryRepository) // Injected in. The correct way
    {
        _categoryRepository = categoryRepository;
    }

    public override ActionResult Index(ParallaxNavigationBlock currentBlock)
    {
        var firstCategory = (currentBlock as ICategorizable).Category.FirstOrDefault();

        var model = new ParallaxNavigationViewModel
        {
            Category = firstCategory > 0 ? _categoryRepository.Get(firstCategory) : null
        };

        return PartialView(model);
    }
}

// ViewModel
public class ParallaxNavigationViewModel
{
    public Category Category { get; set; }
}

public static class Extensions // Needs to be in a static class
{
    // Extension method for categories
    public static IEnumerable<Category> GetCategories(this CategoryList categoryList)
    {
        CategoryRepository categoryRepository = ServiceLocator.Current.GetInstance<CategoryRepository>();
        return categoryList.Select(x => categoryRepository.Get(x));
    }
}