要在Alchemy CMS中使用Cloudinary来为每个站点区分不同的文件夹，并且确保图片没有站点过滤，可以按照以下步骤进行设置：

1. 在Gemfile中添加以下gem依赖：

gem 'alchemy_cms'
gem 'alchemy_cloudinary'

2. 运行bundle install安装gem。

3. 生成Alchemy CMS的配置文件：

rails generate alchemy:install

4. 在config/alchemy/config.yml文件中，添加以下配置代码：

attachment_styles:
  styles:
    thumbnail: '100x100>'
    small: '300x300>'
    medium: '600x600>'
    large: '900x900>'
  default_style: :medium
  path: ':class/:attachment/:id_partition/:style/:filename'
  url: ':class/:attachment/:id_partition/:style/:filename'
  default_url: '/images/missing.png'

5. 在config/alchemy/attachments.yml文件中，添加以下配置代码：

cloudinary:
  storage: :cloudinary
  url: ":cloudinary_url"

6. 在config/alchemy/picture.yml文件中，添加以下配置代码：

cloudinary:
  storage: :cloudinary
  url: ":cloudinary_url"

7. 在config/alchemy/picture.yml文件中，将以下配置代码添加到每个站点的配置部分中，以区分不同的站点文件夹：

attachment_styles:
  styles:
    thumbnail: '100x100>'
    small: '300x300>'
    medium: '600x600>'
    large: '900x900>'
  default_style: :medium
  path: ':class/:attachment/:id_partition/:style/:filename'
  url: ':class/:attachment/:id_partition/:style/:filename'
  default_url: '/images/missing.png'

下面是一个示例配置文件的代码：

defaults: &defaults
  attachment_styles:
    styles:
      thumbnail: '100x100>'
      small: '300x300>'
      medium: '600x600>'
      large: '900x900>'
    default_style: :medium
    path: ':class/:attachment/:id_partition/:style/:filename'
    url: ':class/:attachment/:id_partition/:style/:filename'
    default_url: '/images/missing.png'

sites:
  site1:
    <<: *defaults
    cloudinary:
      storage: :cloudinary
      url: ":cloudinary_url"
      attachment_styles:
        styles:
          thumbnail: '100x100>'
          small: '300x300>'
          medium: '600x600>'
          large: '900x900>'
        default_style: :medium
        path: ':class/:attachment/:id_partition/:style/:filename'
        url: ':class/:attachment/:id_partition/:style/:filename'
        default_url: '/images/missing.png'
  site2:
    <<: *defaults
    cloudinary:
      storage: :cloudinary
      url: ":cloudinary_url"
      attachment_styles:
        styles:
          thumbnail: '100x100>'
          small: '300x300>'
          medium: '600x600>'
          large: '900x900>'
        default_style: :medium
        path: ':class/:attachment/:id_partition/:style/:filename'
        url: ':class/:attachment/:id_partition/:style/:filename'
        default_url: '/images/missing.png'

请注意，以上代码是示例配置，你需要根据自己的实际需求进行调整。

通过以上步骤，你可以使用不同的文件夹来区分每个站点，并确保图片没有站点过滤。