Custom post type isn’t working

One problem is that your 'capability_type' parameter 'community' doesn’t match your 'capabilities' array values.

From the Codex:

capability_type

(string or array) (optional) The string to use to build the read, edit, and delete capabilities. May be passed as an array to allow for alternative plurals when using this argument as a base to construct the capabilities, e.g. array(‘story’, ‘stories’). By default the capability_type is used as a base to construct capabilities. It seems that map_meta_cap needs to be set to true, to make this work.

Your capability type is:

'capability_type' => 'community'

And note your 'capabilities' array:

'capabilities' => array(
    'edit_post' => 'edit_community',
    'edit_private_posts' => 'edit_private_communities',
    'edit_published_posts' => 'edit_published_communities',
    'edit_posts' => 'edit_communities',
    'edit_others_posts' => 'edit_others_communities',

    'delete_post' => 'delete_community',
    'delete_posts' => 'delete_communities',
    'delete_others_posts' => 'delete_others_communities',
    'delete_private_posts' => 'delete_private_communities',
    'delete_published_posts' => 'delete_published_communities',

    'read_private_posts' => 'read_private_communities',
    'read_post' => 'read_community',
    'publish_posts' => 'publish_communities'
),

Your capability type is singular, and your constructed capabilities are plural.

Try changing capability type to this:

'capability_type' => array( 'community', 'communities' )

Also, if you define 'capability_type', you do not need to define each capability explicitly. So, try omitting the 'capabilities' argument entirely.

If your CPT doesn’t appear after that, then the issue is likely due to your Members Plugin configuration:

1. Ensure you have properly defined your custom capabilities
2. Ensure that the current user has the capabilities referenced in the CPT.