We created a post group for members-only content and I created a content template to use for non-members so that they see a message to join the membership to see it. It shows up correctly in the post content area, but the post's comments are still visible down below. I looked in the settings for the content template I created and there is no setting for not showing comments. I looked in every area on the right sidebar to find controls but there are none.
We're using this on existing posts using the regular WordPress posts.
Looking into your website's settings, I can confirm that the Toolset Access post group restrictions are only applied to the content/body section and they don't automatically extend to the comment section.
For example, the following code snippet for the Genesis framework, will check if the current user has permission to access the current post's content or not and if not, will remove the comment section: