Is there a way to hide a user’s posts from their Activity feed?

by

Both the “Iconic One Pro” theme and the “Paid Memberships Pro” plugin appear to be commercial products and the question deeply depends on third party products, either of which should make this question off-topic. However, I think it can be generalized to a couple of options:

  1. A filter on pre_get_posts

    add_action(
  'pre_get_posts',
  function($qry) {
    if ($qry->is_feed()) {
      // your conditions go here
      // I don't know what they should be as all the code is behind a paywall
    }
  }
);

  2. Filter the_content_feed

    add_filter(
  'the_content_feed',
  function($content) {
    // you can alter your content here and return modified content
    // perhaps a note saying the content is behind a paywall
    // like the code I'd need to write a decent answer
    // then return $content, modified or not
    return $content;
  }
);

There are numerous questions and answers here about actions and filters, and especially about pre_get_posts. I think you are going to have to take it from there. My assumption is that the plugin you mention adds callbacks to one or more hooks to control the “paid” vs “free” content display. I would suggest you find where that happens and follow suit. It may be as simple as adding the same callback to another hook or two.