I am guessing that the Memberium plugin adds a filter to the regular wordpress search that excludes/filters out the posts that should not be visible by the current user.
Unfortunately I am not familar with that plugin, and I could not find a free version of it on wordpress.org, but I guess there must be some sort of a function that can check if the current user has access to a specific post or not. Based on that, it should be possible to construct a custom code to do the same for this plugin as well.
If you can add temporary FTP and back-end access to your test environment, I might be able to figure it out. I have found some documentation on their site, but there is very little information about the code itself.Best,
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