[Boone Gorges]

mercime’s suggestion will work well if you want to keep people from commenting on certain kinds of activity items. If you want to turn off updates entirely, you may want to do it at the theme level. You’ll need a child theme (https://codex.buddypress.org/theme-development/building-a-buddypress-child-theme/). In that child theme, make sure you have a file groups/single/activity.php. You can get the content of that file from wp-content/plugins/buddypress/bp-themes/bp-default/groups/single/activity.php. Then, in the version of activity.php in your child theme, remove the following lines:
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