Enabling WooCommerce Members Only ensures that unauthorised users don’t see any content in widgets.
However, if there are certain widgets that you’re happy for users to see, you can just go to WooCommerce > Settings > Members Only and add the widget names to the ‘Widget Whitelist’ field.
You’ll need to ensure that the ‘Enable Widget Whitelist’ option is selected.
How to find the widget name
You can find the widget name by going to Appearance > Widgets. The widgets are each named, e.g. ‘Search’, ‘Recent Posts’.