How to show all items in facet, only allow one selection?

Assuming we're talking about the new Facets as exposed filters:

Using Better Exposed Filters → you can have the facet rendered as 'Checkboxes/Radio buttons' on the filter widget. Disableing the 'Allow multiple selections' option on the facet itself, will get radio buttons.

I was actually asking about the facet blocks.

There are settings for dependent filters within facets, but I think they do 2 consecutive updates, instead of the first just updating options in the second.

Here are some modules to investigate as well:

https://www.drupal.org/project/selective_better_exposed_filters →
https://www.drupal.org/project/views_selective_filters →